If placodonts (cyamodonts) then the teeth are wrong, etc. etc. If
nothosaurs and plesiosaurs, well... um... I'm still looking for some
synapomorphies.
I'll put it bluntly: Only Robert Carroll has the right to believe that
"sister-group" is another word for "ancestor". I know Bob Carroll, I...
uh... met him once, and you, sir, are no Bob Carroll! :o)
Wouldn't something slow and lumbering fit better?
That's just one character.
I'll dig up deBraga & Rieppel 1997 in an hour or two and try to post some
synapomorphy lists and the tree.