Adjustable Spring Bass Traps

Yes, but the hard part is making the trap cover a large enough surface area. Sucking all the 20Hz out at a 1'x1'x1' cube in the room isn't nearly as effective as say floor to ceiling corner trap.

This idea could work.  You definitely want it in a sealed box (vented won't do the same thing).  You will need to put some sort of damping material on the inside back wall to cushion the "woofer spring" and increase the bass trap bandwidth.  The hard part here is trying to determine the "weight" of the passive radiator.  You can try to use a tuned membrane bass trap calculator, but you'll need to figure out the "weight per square inch" of the passive radiator.  Then it's the volume of the internal cabinet.  I think it's much easier to engineer a tuned membrane bass trap because the area of the membrane matches the area of the box and the entire membrane has equal distance to the back of the box.  Not saying this can't be done, but it is entering into engineering rocket science here.

I have only seen one active bass trap made and it is called "Active Bass Trap" made by a company called Bagend.  It is similar to the type of technology you find in noise-cancelling headphones.  It uses a microphone mounted on the front of the cabinet and then uses a small amp with a 10" woofer to create the opposite "cancelling" waves.  I have read that it's somewhat effective.  You may need 2 or 3 of these.

You may be better off doing a design where your rear corner subs are fired in opposite polarity of your front subs.  I forget what this is called (something like "double-bass" or something).

I've seen subs that double fire. Isobaric, and daisy chained.  The active driver on the inside of the chamber is fired out of phase.. They dig pretty DEEP.. Face to Face in an open baffle is pretty impressive too.
It's always the same with bass, distortion. Not hard to make a lot of BASS but GREAT bass in a room is tough... Back walls are BAD.. Retracting walls? 007 stuff...

Regards