Take a look in Trade-A-Plane. There is a company that sells overhauled
and remanufactured engines at $ 300 over cost.

A factory reman O-360-A4M is $19,690 that would be a zero time engine
with a new log from Lycoming. A Teledyne overhaul is $ 15,050. (These
include exchange)

You minimize the down time and you will get a "brand name" for the o/h.

The company is Air Power Inc.

Good luck