---- it appears it is the "Engine on Condition" that is the sticking point.
Probably because the Flying School doesn't know what they are talking about ---- or a prejudiced against what most of the rest of the world have always done, and we have done in Australia for something like 15 years.
Remember ---- it is RECOMMENDED TBO, by the manufacturers, as far as FAA (or whoever) is concerned, it is just that, a recommendation, it has no regulatory force.
Indeed, the Australian practice of enforcing the R-TBO for commercial ops., and canning the many life extension extension programs that existed for many years ---- long before AD ENG 4 ---- is a direct result of the CASA lack of depth of knowledge re. piston engines, consequent on the retirement of the last bloke they had, who had real in-depth knowledge.
There were plenty of Chieftain engines running close to 3000 hours, there are plenty of C-152s in flying schools with upwards of 4000h on the engine.
Find another school.
If they are "head in the sand" (or somewhere else quite dark) about this, they are probably as ignorant about a whole range of things you need to learn.
Tootle pip!!