Here's what I found out. Took off left pedal. Dust cap came off with allen wrench. There was a nut on the outer end of the spindle. Took it off and pushed out the tapered spindle. There was a cartridge bearing at the end of the spindle just under the nut, but the bearing stayed in the housing. Cleaned it all up and greased it. All went well.
Removed right pedal. Took off dust cap. Tried to remove nut on end of spindle but something was wrong. Turns out, the right side spindle has left-handed threads on the outer end of the spindle. So, I stripped the 10mm nut trying to get it off. Perhaps if I can find a replacement nut I can salvage those pedals.
Now I don't feel so bad about placing an order yesterday for new pedals.
You live and learn - or don't, as someone has said.