Most compressors do NOT use centrifugal switches, but a ""starting relay""
which appears to be a time delay that opens milliseconds after power.

If in fact the starting winding is getting power (easy to check)
and the compressor is stuck; then look to the "hard start kit"
approach which is in reality a lower value capacitor [less Xc to
limit current].

I'd likely try paralleling a cap equal to the existing one.
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