Dissapears after 1600 rpm, my buddy's uncle thinks it could be the oil pump is going bad and not getting enough oil at low rpm, does this sound like a likely problem/ fix if I replace it

We recently did a motor transplant, since that time, the shifting is very sloppy and now it is popping out of 5th gear and reverse is very hard to get into. I believe there is a bushing in the shift mechanism that may be the problem?

My 1993 MX-3 failed the low idle hydrocarbons test at the DMV. Can anyone help me with this problem?
(I am unemployed and cannot afford the $800 estimate that a garage gave me to replace the spark plugs and the oxygen sensors. I was told they needed to be replaced due to oil leakage.)

Thank you, very much.