I'm back in laundry business! Sears guy had the pump the washer needed actually on his truck. Parts + labor was $160 - that sounded better than replacement. He did warn me that some seals are leaking - a sign of age - but that the machine might last five or six more years.
I'll have time to go into therapy to deal with my unusual attachment before I have to give up the washer and dryer forever.
And the repair man found a buncha cat toys underneath - now the kitties think he's a cool guy.