But I'm thinking; Is there a way to tighten a tee nut with a cam,
wedge or whatever from the side of the adapter plate? The idea here is
to keep the adapter as low profile as possible.

Of course! But there are 'costs'. You'd have to slot the bolts,
foregoing strength. You'd have to 'collar' them to make them captive to
actuator wedges... you'd... Oh... you know... it goes on and on.

Why not just build a couple of adaptor plates that DO extend out past the
perimeters of the things you want to bolt down? Bolt one to the back of
the chuck using the existing blind holes, then bolt the plate to the
table (rotary or mill table) with tee nuts/bolts as usual for fixturing
parts. If necesary, duplicate the method on the face of the rotary.

'Hate to say it, but I think I spend more time mounting stuff than I do
machining it!

Lloyd