That vacuum hose on the carb you re-installed if I’m interpreting your photo correctly, it appears to be a ported vacuum source, from above the throttle valve in other words. That signal would usually go to the distributor to advance the timing on accelerations, to the EGR (often via some coolant temperature switches), and possibly to the transmission. Ford had both one input and two input vacuum modulator designs in that era. If you have the two input type then the above would apply. It might be when you re-connected it, it advanced the ignition timing and that is what caused the pop you heard. Maybe you got a little ping or backfire into the intake manifold or something. Normally that wouldn’t do anything at idle tho, as there is little to no vacuum from a ported source at idle. You could measure it I suppose. I expect you’ll find there’s no vacuum there at idle, but significant vacuum when you bump the accelerator.
Suggest you also connect a hand held vacuum pump to the line(s) which supply the transmission vac modulator valve. They should both hold vacuum to 20 inches. If not, you got a leak in those lines or the modulator itself.
It appears you got some cyphering to do there OP. On that era Ford 302 the vacuum line configuration is very important to have it all connected correctly. Until that bunch of spaghetti is all correctly configured, it doesn’t make much sense to try to solve other engine performance problems. I suggest as your first task that you post a diagram of how it is configured now. Look around in the engine compartment, see if you see a vacuum hose emissions diagram somewhere there.
The experts here helped me w/a similar vacuum line configuration problem on my own 302 equipped truck, here’s the link. At the time I included a line-drawing of the configuration that I updated a couple of times with corrections, but for some reason that diagram has been deleted. Perhaps uploaded diagrams are only stored for a certain amount of time on the Car Talk server. At least I don’t see it when I look at that thread. If anybody here knows how to resurrect that diagram, the Lincoln owner OP of this thread would probably like to see it.