I just finished crafting an application's cover letter for a particular lab (if it matters, area of research can be broadly classified as computational social sciences). The situation is that they have several postdoctoral positions and I feel that I am a pretty good fit for either one of them (how modest ;-).
However, I think that it makes absolutely no sense to send three separate cover letters for each of the positions, as 1) they are affiliated with the same lab (and, even, one of co-PIs is the same for all of them); 2) the positions share a lot of subject domain areas (I, actually, expressed this point directly in my cover letter - I hope it will not be considered offensive or otherwise inappropriate).
Therefore, my two related questions are:
Would it be appropriate to submit a single application with a single cover letter to those positions, based on my points above, even though they are advertised separately?
Is it acceptable that my cover letter (that single one) is almost two pages long (including all appropriate vertical spacing and 12pt font size - trying to be gentle with the readers' vision)?