I know we’re peppering you with questions, so please take no offense. It’s just hard to decipher things sometimes without being there. If the new engine is causing the shaking to this degree, it will probably (or has already) set a check engine light diagnostic trouble code. If so, please let us know the code. I would check everything that “holds the engine in place,” the 2 dog bone mounts at the front of the vehicle, both engine mounts (previously described). Be sure to check all of the suspension related fasteners, from tie rod ends, sway bar bushing, power steering rack and pinion unit mounting bolts, etc.
If the vehicle is shaking at a stand still, you can rule out the tires and quite possibly the suspension components too (tie rods, sway bar, etc.,)
It could be a bad vacuum leak resulting from the engine swap procedure. A gasket such as around the plenum might be leaking and causing this shaking,ignition problem, something left unplugged etc.,
One question for you this time… Does the shaking continue throughout the driving range and all rpm’s or does it disappear at certain speeds?
One way to test the tires, is to get the car up at a good speed and carefully switch into neutral. If the shaking then continues, the tires are suspect. Being that you purchased new tires, it could be as simple as a tire out of balance. This happens regularly…
Thanks for the update. Keep us posted