They are not Konis.
Well, my policy is: If appears I can't fix it, then FUBAR it.
I WD-40'd the piston rods and got my wife to get on the bike with me, and play Buckaroo. After some serious bouncing (seat held up good), I noticed the bike sat lower.
In a minute or so with the bike on the C/S, I heard what sounded like wheel spokes pinging (oh crap, I tore up the wheels!) only to see the shocks popping back to the 13 1/2 " they had been all this time. Did it 3 times, with a little bit more free movement each time.
I don't know how much they compressed, but at least I have some movement now. Maybe I just need to ride the snot out of it to get things loosened up a bit?