I have also seen a really goofed up 4K engine, similar complaints from owner (long time ago in Karachi when I used to run a mazda 808) - owner of said corolla was a freind of my father and he begged my father to make me repair his car, as he found my 808 really fun to drive.
anyway, long n short, I found that the camshaft timing was a tooth incorrect and the mechanics had keyed the distributor wrong to mask that slack, they also had messed with the rockers.. result = bad engine run.
the engine was cooled with well water I think, it literally had mud in it. - coolant at that time was sold in a seiken metal can or sometimes in a metal can made by PBS (Pakistan Burma Shell) - it was the oldschool green coolant.
Had to take apart the engine top and front timing case to repair it, the rockers and carby were shot to hell - replaced it with replacement parts from shershah, rebuilt the dizzy and replaced ignition coil with a good spare I had lying around. At finish the car was very sweet once again.
The remarkable thing of the 4K engine was that it would even run in that pathetic state.