Valve guides / stems would have to be very bad and valve seals missing to have liquid oil coming from the exhaust.

Given the previous engine " rebuilder" didn't tighten a connecting rod cap beyond finger tight, I vote for a upside down / missing / broken piston ring. If you do have a broken piston ring, running it will damage the cylinder wall.

As I stated in the other thread, take the engine completely apart and check everything.

Once you get everything fixed, don't run the engine without a load because the cylinder walls will glaze / engine will burn oil and rings won't seat in for a long time.

Loading the engine consists of idling just long enough to get up to temp then ,while driving, accelerate the car at 20 % RPM and load ( throttle ) then close the throttle and slow down. Increase this in steps to 75 % or so then let the let the engine cool. There is no need to rev the engine any higher than what you would do pulling a steep hill.

The object is to build cylinder pressure so the rings are forced outwards against the cylinder walls.

Why are you worried about overheating? What is wrong with the cooling system?