Not sure about flat-fees since a lot of independents charge based upon the cost of parts..
Not sure why you WANT a flat-fee as this tends to hurt you if it's a simple fix and doesn't cost a whole lot...
I trust this guy Dave (ebay="daveds50" if you want to see his feedback/repairs/resells). Fixes electronics for a 6-figure salary. VERY knowledgeable and very quick turn-around time. Sent him a Sony CDX-C910 and was fixed/sent back to me for a VERY fair price and in less than a week. PM if you want his email.
Otherwise, http://www.kbaudio.com is a favorite as well. Sergey is very knowledgeable as well...
Many thanks for the ideas. As for the flat-fee, most appear to be between $65-$109 including return shipping. Are there places that would charge less? I figure a minimum charge would be about this anyway, no? Thanks, again....