It sounds like a carb/tuning issue to me. The clutch should make the sound even sitting still, and a small pop or backfire in the exhaust when shifting between gears isn't that uncommon. I think you are on the right track in thinking it is slightly rich, and the AIR system (smog pump) is actually putting air/oxygen in the exhaust just like it should. In this case I think there is a drop in pressure in the exhaust when you let up to shift that lets the air/fuel pop off.
Things to check:
Coasting richer system- a set of switches that open/close a valve on the carb that lets a bit more fuel in when the clutch is not pushed in, the gas pedal is not pushed in, and the trans is in 3rd or 4th. If that valve is just open all the time or not closing when the clutch is pushed in that would create a slight rich condition. It is somewhat hard to test all these things working together, but you can test each switch pretty easy.
Timing, points, etc - general tune up stuff, anything that might make it not run 100% would leave some gas unburnt going out the pipe
AIR System/Smog pump - there is a vacuum switching valve and some other parts involved in the AIR system that could make it pump too much into the exhaust. Might be worth trying just bypassing it to test. Pull the belt, or better pull the hose off the AIR manifold that goes into the head just above the exhaust manifold. Plug the manifold off (you could pull the hose from the pump and plug it with a large bolt if its hard to find something to plug that large port on the manifold) so that air can't get in and exhaust won't leak out. If disabling this does cure the popping, it could still be fuel related and this just provides the air for the bang.
_________________
95 Isuzu Trooper Daily Driver
86 Isuzu Trooper reliable backup
77 LUV 2wd stock beltway blaster (resting)
79 4x4 LUV project: 2.6L, 5spd, 31s (eventually)
MEPR: Man, my 4x4 makes all other LUVs look good
