I believe we've talked about your amps before, but I don't remember many details so I'll treat this as a completely new thread. (It should probably be moved to Legacy Products, too - I don't know how to do that, but hopefully one of the other guys will do it.)
Actually, the ParaSEX was the fourth - and last - version of the 2-tube monoblock S.E.X. amps. And there were two variants of that. They are easily distinguished by the power transformer, the deYoung with many colorful leads, or the Magnequest PGP8.1 with solder tabs.
In both cases, the original plate choke has a secondary winding in the output cathode lead, providing a few dB of feedback. If you have the MQ choke, you have probably connected the cathodes directly to the bias resistor.
There are several possibilities for the pops and bangs, but I need to know what power transformer and plate choke connection you have before I can say very much more. The easiest one to check is to swap the tubes between amps, and see if the noises go with the tubes or stay in the amp.
By the way, one of the known issues is that cathode resistor, which should have at least a 5-watt rating, so I am actually surprised it has lasted this long. It is probably the wrong value anyhow, but I need to know which power transformer you have before I can comment further.