Not Corolla to celica swap, did corolla to corolla swap
I gots the 1.6 hatch 97 corolla, one year out of your criteria lol, sorry. (small front discs, rear drums)
Went to wreckers, found a 97 corolla RV (the same hatch, but 1.8 engine).
Bought the whole rear braking system on it. Bolted straight on to my car, and made a fair bit of difference. Then bought the front brakes and installed them as well, made a world of difference...and it was cheap too and no conversion hassles etc.
Weird because i would've thought the RV's front discs would've been the same as the 1.6...but it wasn't.