NickL, this may sound like something I've heard before about the Accord (I'm not really knowledgeable about the Accord, so my recollection is vague)
My advice is to go on Accord forums, and search for this topic. Also, there is a CanadianDriver review on your generation Accord (Used Car Reviews) that lists common problems noted on forums.
The reason I recommend this is because, sometimes, when a problem reaches a certain proportion, there are "secret" warranties out there (for all car manufacturers) and people who have obtained a copy of the actual secret warranty bulletin (or have even printed out pages of people noting the same problem in their own cars) have had success in having their problem acknowledged and fixed for free.
I think your initial thoughts about how to proceed are a good idea though, and should be tried first or in parallel.