You checked and the bolts for the engine mounts are installed, right?
And bolts are in the transmission mount and cross member, right?
Come on guys. Remember, check the things that are easy and don't involve any cost first. Doing this will take a few minutes and if things are OK, then move on. Process of elimination.
I actually think there is more than one issue, but without seeing this "wobble" in a video or in person, it will be hard to diagnose.
Agree w/Bryon. When I learned OP used non AC plugs, that sent up a red flag to me. I used to think plug brand did not matter, I mean, a plug is a plug, right? Well, I have had many instances where an engine just would not run or run right with certain brand(s) of plugs. Not even sure what it is that causes the problem, but I know it happens.
Couple of years ago, my cousin tuned up his '39 F20 Farmall (antique tractor). It would not fire,(hit a lick, if you are from Appalachia) so he calls me to bail him out. This is a hand crank magneto engine so patience goes away quick if there is no firing of the cylinders. I told him to put the old plugs back in and what you know, it starts. Autolites were the new plugs. I told him, they just will not work in that type engine. Made a believer out of him that day.