Ask Dr. Free-Ride: How should I address multiple doctors?

I have, of late, received a number of emails asking advice on matters somewhere in the territory between ethics, etiquette, and effective communication with members of the tribe of science. While I’m no Ann Landers (as has been noted before), I’ll do my best to answer these questions on the blog when I can, largely so my very insightful commentariat can chime in and make the resulting advice better than what I could generate on my own.
Today we have a question from a reader struggling with the question of how to address one letter to two doctors. He writes:

Hi Dr Free-Ride,
I’m not sure if this is a topic that falls within your normal scope of
interests but whatever advice you can provide would be appreciated.
For personal (ie non-academic) reasons I have to address a letter to two
medical specialists who work in separate but related areas. They are
co-operating to a greater or lesser extent in investigating a family
health problem as well as taking individual approaches according to
their specialities.
Each is attached to a different hospital and each is head of their
department. However, one has the title Associate Professor whilst the
other has the title Professor. The A/Professor is a female and the
Professor is male. Based on the first letter of their surnames lets say
that we have A/Prof L. and Prof M.
A/Prof L. is, apparently, doing more (maybe most) of the work at the
moment but she is not very communicative (ie. despite far too many
attempts at contact we have heard nothing from her) whilst Prof M. is
quite active in the matter also and maintains at least some contact.
The problem, obviously, is the address and the salutation.
One solution seems to be that I should send the same letter individually
addressed to each of them with an indication (cc: otherdoctor) that the
other person has received a copy. I’ve got some fuzzy thoughts as to why
I don’t like that solution but I’m having difficulty in writing down
those thoughts.
I could address the letter in strict alphabetical but that seems to
“promote” A/Prof L. and it would seem natural to write the salutation as
“Dear Madam and Sir, …” which adds to that appearance. I did consider
“Dear Doctors, …” but that seems to be ignoring their professional
titles which I think is not a good idea.
Of course, I could reverse the address and therefore, as I see it, obey
the academic hierarchy but as each are heads of department in their own
right I’m not sure that my understanding of the hierarchy is correct.
I’m also concerned that A/Prof L. would read this as not respecting her.
So, I’m rather confuzzled at the moment.
If you are able to un-confuzzle me I’d be very grateful!
I know that you sometimes use received emails as blog material and you
are very welcome to use this email if it is useful to you.
Thanks for your time.
Ivan.

I’ll admit that my first thought was to go for the same letter addressed two ways, with the doctor to whom a particular copy of the letter is sent as the addressee and the other doctor (who gets the other version of the letter) cc’d. Like Ivan, though, I decided that I don’t like that solution. First off, going this way introduces the practical risk of mixing up letters and envelopes, leaving each of the doctors in question receiving a letter on which he or she is cc’d but not the primary recipient. This would, of course, be the opposite of what was intended, and could potentially leave each of the doctors feeling less directly involved and responsible as far as the query in the letter, and perhaps even as far as the family medical situation more generally.
Indeed, even if you got the right letter in the right envelope, I think this addressing strategy tends to reinforce the idea that the two doctors are interacting with the family medical situation separately, rather than in collaboration. I take it that one important reason to write to them about this situation together is to help them actually collaborate in dealing with the situation, and with the interested family members (including Ivan writing the letter to them).
So, the easy answer having been shot down, I think the important question to ask is what is the best way to construct this letter to get these two doctors communicating effectively with each other and with the sender?
Especially in the case of Associate Professor L., who is presumed to be working hard on the case but who has so far not been in contact with the family about how this work is progressing, the hope is that the letter will result in communication — that she will update the family on what she has learned so far, what work is still in progress, what sort of timeline she imagines for having enough information with which to make some reasonable decisions about the health situation, etc. The letter needs to communicate to her that the family needs her updates — not because they don’t believe she’s working on the case, but because this information will be more comforting and useful to the family in getting through the situation than will continued radio silence.
Professor M. has maintained some contact with the family (although perhaps not providing as frequent updates as the family would like). The letter needs to leave Professor M. inclined to keeping the family in the loop as he works on the case.
Potentially, the letter can also put Dr. L. and Dr. M. in better communication with each other on this family health problem. Although they work in different areas and at different institutions, they may find this professional collaboration on this particular case productive. They may be able to share relevant articles or case reports they turn up in their own literature searches, or possibly fruitful ideas that the other has better expertise to evaluate. Indeed, collaboration on this particular case could lay the groundwork for future productive collaboration between the two doctors and the departments they head.
Plus, if Dr. M. is in regular contact with Dr. L. about this case on which they are both working, there’s a chance he can communicate to the family about what he knows of Dr. L’s current progress. It’s possible that Dr. M. is just more comfortable communicating with the family (or with patient families in general) than Dr. L. is, making him a more reliable conduit of information. This is not to say that Dr. L. shouldn’t be working on communication skills or has no duty to keep the family up to date on her progress. However, training one’s doctors in such skills and duties can be tiring work. Pragmatically, having a reliable way to get the information (via Dr. M.) is better than getting no information at all.
Where does this leave us as far as addressing the letter?
I’m not entirely sure the recipient address and the salutation are sufficient to communicate what needs to be communicated (with respect to the family’s desire to be kept in the loop with regular updates from both doctors, and the family’s hope that the doctors will collaborate with each other to find the best approach to the family health problem in question). There may need to be some explicit communication of this in the body of the letter itself.
As far addressing both recipients with proper honorifics and recognizing both for their expertise and accomplishments (as heads of their respective departments), I think it would work to address the letter:

Herfirstname L-lastname, M.D., Associate Professor and Head of [Her department], Her Institution
Hisfirstname M-lastname, M.D., Professor and Head of [His department], His Institution

To my mind, this recognizes the (slight) difference in academic ranks, but doesn’t make a gigantic deal out of it, emphasizing instead their positions as department heads — and the special disciplinary expertise from those different departments that each of them is drawing upon to work on this case.
Alphabetical order seems as fair as anything else, and having the less-communicative Dr. L. listed first may gently put her on notice that the family needs a bit more from her (at least in terms of communication) than she has given so far.
As far as the salutation, my first preference would be:

Dear Dr. L. and Dr. M.

especially since medical types seem most comfortable being addressed as “Doctor” (and somewhat discomfited by holders of mere Ph.D.s who introduce themselves as “Doctor”). But, it would also be appropriate to use the salutation:

Dear Prof. L. and Prof. M.

I have never, ever seen “Dear Assistant Professor X” or “Dear Associate Professor Y” as a salutation. The convention seems to be to identify the precise professorial rank in the address block, then address any flavor of professor as “Prof.” in the salutation. Because this is conventional, neither Dr. L. nor Dr. M. should be jarred by it.
I hope this helps Ivan with the problem of addressing the letter — although I’m probably adding at least a paragraph to the body of the letter to explicitly address the collaboration and communication Ivan is hoping not to undermine with the address and salutation.
Commenters who have other suggestions here (especially if they think the advice I’m offering is wrong) should share them in the comments.