I thought about insulating it myself... Wrap the pcb in plastic, stick it in the case, fill it with foam insulation... that could be messy though.

I found several other suitable replacements, however, I can't find them in stock anywhere and I've checked Mouser, Newark, and Digikey. Here's a short list of known quiet relays that will fit...

Fujitsu FTR-P1CN012N (obviously)
NAIS/Aromat CQ1-12V
GEI AR7-012-CQ6S (made in USA! well, company is in NH)

Oh, and here is a great table I found on CIT's website. http://www.citrelay.com/Relay%20Cross%20Reference.pdf
Nice spelling job on the title.

I've found plenty of others that are equivalent to the NEC's at Mouser. If anyone wants to go digging around for relays, make sure you look at the current rating, that's pretty much the only spec that vary's in all of the compatible parts. A replacement should be rated to carry at least 20A for 1 hour.

I'll likely try to just put one of the fujitsu relays back in for the front wipers. I'm not sure which fujitsu relay was bad, so I have a 66% chance of putting a good one back in.

My alarm/wiper board looks like the picture in the link above posted by Amigo2K. In that pic, I'm assuming the relay already replaced by the NEC is the rear wiper, and the one circled is for the front wipers? I need to know which one to replace with the Fujitsu. Does anyone know what the other relay is for? Alarm system probably right? I think I'll leave the NEC in that one.