Yes, the switch can be taken apart and refurbished. Save that for your last option.
confirm you have 12 V at the starter relay. I don’t know the testing process you used to bypass the starter relay but if there is voltage there and the relay is good, the starter should engage with proper jumping .
however, Jon Haas has recently shared with me that he is aware of brand new starter relays being DOA out of the box.
Larry