I never got anything like an apology from Mike, but after Arody and Tod took charge of the situation, I had a new washer delivered and installed in less than a week. RPM has also expressed the desire to refund me the $80 I spent at the laundromat while the washer was broken, which is a nice gesture.
I'm still disappointed that the issue took over a month to fix, but once I got the attention of people higher up the chain, the problem was solved very quickly.