This morning I took to investigating the cause of the rattles and clunks. It turned out to be the new transmission mount. It has about 3/8" thinner rubber than the old one I was replacing. That made the transmission and transfer case sit lower, which caused exhaust pipe to sit about 1/8 of an inch from the crossmember. I put in the old mount, and the exhaust pipe now sits about 3/8 to 1/2 an inch from the crossmember. No more rattles and clunks from the exhaust hitting. But these beefier engine mounts sure accentuate any imperfections in the way the engine runs. I think mine is running smoothly for having over 200k on it, but it sure rattles the flimsy stuff like trim and loose windows now. Going down the road I can tell it is more stable with not having the engine moving around as much. But sitting at a traffic light it has a low rumble-vibration that it didn't have before. Once these mounts soften those rattles and vibrations should go away.
assuming they were not binding and were not being pinched by the smaller t case mount, like, if you had them installed and then changed the rear one on t case without having all 3 properly rest on them then fasten at that point. Ground outs from exhaust will also do this like you said you had before going back old one(is it worn?) a worn mount with two fresh ones is a good recipe for that mount to accentuate an issue because the other two started being more solid and like new but the one on t case is ideally supposed to be that too, to work together. this is more an issue in newer vehicles with complex mounts, but basically in my car, for example, it has 4 mounts and two of them do the most heavy work for the system. one is a torque axis mount that is engine mounted near crank(v6) and the most important trans one is a single one in front of engine bay that prevents rocking back and forth, which is the natually movement of the crankshaft and everything in the engine. the wheels turn from shafts that rotate in that same plane. The other two are more for vibration and torque steer/keeping the drive axles planted because like a diff sometimes, it naturally wants to roll up and put extreme angles deflecting from torque or something sciency sounding.
in your truck, my truck, our trucks. Not so complex thankfully. I would see about another thick mount or at least right away verifying your hangers for exhaust are properly isolated. And then your drivetrain is setting not-binding but also your exhaust isnt either. if you, for example, hang it and you move your engine later then you are loading those mounts and isolators different than what harmony would be like. also does your exhaust pipe extent all way out back or near back but side? if undeer truck that can be why and you also may have something or just things resonating at the frequency of your engine running and its enough to actually cause that. wheel tubs, bed bolts good, cab mounts good? Doors not loose, any headliner? Hows the hood when closed nice and latched no wiggle, etc. shock absorbers good? A v8 should be better usually, thats good, but it can get downright creative hunting force variations. weather seals good?
I would do the first few good checks, and then also maybe do compression and vacuum test on your engine. you sy its tired right? Maybe you got some power balance issue and its crankshaft which is obviously going to eventually wear bad just on its own bearings but usually the things attached to it dont like that well. If you had a noisy valve train maybe check them pushrods on some glass or make sure the spring and securing is all proper, certain vehicles esp when they have like strong valve springs are pretty known for making real audible noises that would prob shake things a bit. Also consider if you have noise and vibration that if they have a direct correlation to crankshaft or engine speed (nvh wizzards help right lol) then make sure the other noise/vibration is not possibly caused byt something that would make its noise or shakes at the same frequency. like someone with a wheel balaance issue that based on drivetrain and tire sizes worked out to be related to valve train I saw as a example in a video from the 90s. Hard to say if that happened lol.
but i believe in you. If you want to test exhaust and maybe spruce it up some if you are into it, a resonator is dirt cheap and can be a cherry bomb at its simplest and you can add that in anyway you need. but the idea would be youre changing the frequency( i think) and if its resonating and causing a lot of other stuff, that will break that cycle if its main one and you would maybe have no issues.
I hated my buick once. the ps return hose and a tire balance issue both made it seem really bad like alignment or something is broken. but the ps hose ground out(Hey hows those?) is especially more perceiveable with a non submerged system, a long, hard line return(Not on squares much) and either high pressure, too much flow, etc. If you have type 2 pump its not submerged most likely but its flow at rpm should be more manageable than P and CB pumps. but if its pressure is super high, that stuff can cause what i suspect a seat feeling or a wheel feeling .