I have a 2001 Miata SE (6 speed and some other unique stuff)
and other than the lack of power of the other cars you noted i cant imagine a better handling vehicle. For $5k i am sure i can put a turbo or supercharger in and give me performance at par with a boxter (which i babysat for a friend of mine for a few weeks befor i got the Miata...very sweet )

Mine is BRG with 16" wheels...and as we all well know a ghost in the machine which wont give me peace when it comes to whine through my sound system!

It seems like you have had no other issues with the car...a cheap solution would be to just put another engine in it and sit back for 10 or so more years!!

Good luck on your search!