Since my wife was out of town when this happened, I had no choice but to have her take it into the dealer to be repaired. Apparently the problem with the first wiper motor (and the new one) was the wiper gearing mechanism. It was putting too much strain on the motor and causing it to overheat. Both parts were given back to me and I will check to see if the motor is covered under warranty and whether I can get my money back or at least a new motor that I can turn around and sell.

An expensive lesson, but next time I will look more into the cause instead of just fixing the symptom.

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1994 E320 Cab (mine)
2001 Chevy Suburban (wife's)
1995 BMW M3 (son's)
1989 Volvo 740 GL (extra car--for sale)