"every time the needle breaks, it throws the timing wheel out."

But why are needles breaking? I sew, and I haven't broken a needle in a couple of years. You aren't trying to sew over pins, I hope. It's not worth the risk.

Is your machine an unusual one? My mother had an awful time with a commercial machine until a repairman showed her that the correct needle was a tiny amount (maybe one millimeter) longer than the needles she was using.