Test the compressor windings with a meter before touching anything else, that's what saved me after a similar wasted trip. Check start to run, run to common, and start to common against the spec sheet, and if the numbers are way off or open, you know the compressor is gone before you pull a single part. Takes two minutes and stops you from eating the cost on a relay that was never the problem.

Skip it, save the cash, sellers fix stuff anyway.

Mine hates north windows too, all my plants do.