alright there man lemme see, i had the hot start problem which went away not sure exactly what i fixed but i can give you some shit to look at
i've heard running injector cleaner can be bad for your seals. i would take them out and have them all cleaned and blue printed, or if ur going to upgrade secondaries, now is the time. There have been problems where the fuel pump wire is just old, there are several write ups on rx7club.com and teamfc3s.org to help you with rewiring the pump and making sure its receiving all the voltage.
hot start problem also some people say it points to low compression, with 83k(or whatever) on the motor that definitely might be a problem.
I had my fuel injection relay fuck up, i even had to get towed it was a hard feeling to describe but sounds similar, there isa metal box with 1 screw holding it on to the inside of the driver side fender inside the engine bay, after driving a while touch it and see if its very very warm(or when ur car feels like its failing) very expensive peice at the dealer but very cheap at the junkyard btw)
fuel filter is a good idea. but probably not the problem.
TPS (throttle position sensor) it is a bitch make a test light or use a voltmeter, i have yet to be succesful in testing with either of those two the only reason i got it right was B/C i used my SAFC to adjust the TPS. I think ihave an extra TPS laying around.
as far as stuttering check and make sure your throttle plates have free movement, they suck maybe do the throttle body mod while ur at it.
takes a while but once u get all the lil probs out of it u'll love it.
if i think of anything else i'll post, also if you need help don't hesitate to ask. btw if you do a compression test make sure the car is warm