If your cooling system is in proper working order, it is adequate for an N/A Car. The problem/TSB for 96 Cobra's had nothing to do with the radiator itself, it was the density of the AC condensor in front of it. The TSB replaces the condensor with the later unit.
It sounds to me like either your water pump isn't working well, or there is blockage or air in the system somewhere. My wife's 97 has a Stant superstat 188 degree (stock temp to my knowledge) and a completely stock cooling system, and the temp hovers between 195 and 200 degrees (low speed fan kicking on/off) pretty much all of the time. FWIW, 195 degrees on her car is between the M and A on NORMAL. She always thinks it runs hot, but reading the EEC and using a temp gun both show 195 degrees, which is perfectly normal.
Burping the system is very important and can be difficult on these cars. The factory plug is often seized badly. I simply remove the hose from the front of it (below the plug), then drill and tap for a 1/4" NPT pipe plug in the larger plug. It is soft metal, it drills and taps easily. Then I reinstall the hose, and I'll use a small funnel to fill from the burp hole as well as the cap on the expansion tank. Usually this leads to a very quick burping after the engine is started, if it needs it at all.
I should mention that I did drill a 1/16" hole in her thermostat, in the flat flange where it's exposed and not covered by the O-ring. This helps coolant equalize temps on both sides of the thermostat and makes it warm up more evenly.
