15A air compressor blowing 15A breaker
I think you need a bit of “headroom” so a new circuit with the 20A breaker should do it.

For both breakers to run the same amount of time seems to suggest both are functioning correctly. The regs I usually consult gives times for breakers to act if the load is close to the rated value so it sounds like those two 15A breakers are just being run close to the edge and tripping due to an extended time.

I would definitely test it with a 20A breaker - safely though...