Minor update...

I called Singapore Air and requested seats; the agent said she put in my request.

I asked if I could check in online within 24 or 48 hours of departure and pick seats then but was told no, that I could only check in at the airport.

She did give me a PNR I could use.

I went to Singapore Air's website and enrolled in the KrisFlyer program.

Using that account number, I was able to (eventually) pull up the info for my reservation. As whistler814 said, there was a problem with how my name was listed in their system: they had it listed as FirstMiddle Last (no spaces between first and middle, all in the field for "first"). Once I tried the conflated FirstMiddle, then the the record came up.

Unfortunately, there's no record of my seat request. :/

I'll give it 24 hours, check again, and if the seat request doesn't show up I'll call back and ask again.

My concern is being able to get assigned seats before we show up for the 2nd leg of our long trip: we're leaving from SEA at 7:45pm on a United flight to SFO, arriving in SFO at 9:45pm; I assume that United won't be able to do anything about our seats on SQ, and we would show up at SFO about 3 1/2 hours before the SQ flight leaves...don't want to show up in SFO and be told there's nothing but middle seats left.

Oh well, the adventure continues. Sheesh, this shouldn't be that complicated...