My thanks to all who responded regarding my sticky,
unswivelable swivel seats.  Based on your suggestions,
for each seat I:

  - Slid off the seat.
  - Unbolted the swivel plate.
  - Cleaned off the old dirty grease.
  - Re-greased with white lithium grease
    everywhere that anything rubbed together.
  - Re-bolted the swivel plate, and tightened
    the nuts to one full turn less than "fully tight".
  - Slid the seat back on.

They now work great.