Interesting project, looking at something similar
Couple of points on the circuit:
Power Supply:
LM78xx normally have 35v max. This can be problematic with a voltage surge on shutdown, would be inclined to make the cap say 63v and stick a 20v zener in there.
Op amps
A DC gain of 273 might be stretching it, I would be inclined to use an instrumentation amp in there to avoid hassles like device selection. Probably doesn't really matter what, IIRC last time there were some INA 118's floating around and they worked OK.
(Not an electronic engineer but employ some.)
Also may have to go to shielded stuff on the thermocouple wire if there are too many problems with a noisy environment.