If you are not comfortable with your doctor, or even remotely questioning his/her ability...it's time to fire them and find a new one!
First, the Excedrin is working as well, if not better because they ARE rebound headaches. If they were migraines, the triptans would work better. And NO, not all headaches are migraines!
I think you are doing the right thing, reading up and doing what you need to do to get your questions answered. Reading books, doing research online and finding support (US!!!)
Rebounds: you need to completely be off of EVERYTHING for at least two weeks...now, as far as how to do that, IS something you need to discuss with a qualified professional, which one is up to you. I have written some information on a few of the threads regarding rebounds.
(I am NOT, by any means a professional, however I have dealt with this for 14 years and get all of my information from professional resources and would not post it here unless I had some solid backbone to go on...saying that much...I know that the rebounds can be as bad as migraines themselves. I suffered with them terribly more than once for legitimate medical reasons, one time...I had kidney problems and after being on continuous pain meds I ended up having horrible migraines and rebounds!) They are not at all fun, but getting them handled sooner than later is the best situation.