Two of the hard-to-reach captive nuts broke away from the metal that are used to attach the knee pad. What can be done to keep a nut over the holes where the screws go ?

Stick a little windshield butyl on the nut to hold it in place.

Good idea ...........

Same thing happened on my car. Tried the butyl but it kept popping off. Was hard to get everything lined up perfectly. I ultimately just got longer bolts and some washers and reached up and under to get them together.

Or google "cage nuts" and you'll see a bunch of options. They're used a lot for electronics racks. But I haven't seen the weird rectangular ones that go under the dash. My guess is that a square one will also work, as long as the width is the same and it compresses into the hole correctly.

Those cage nuts are removable.
They probably spin because the screws were cross threaded.
Remove the knee pad. Remove the faulty cages by squeezing the tin flanges towards each other with a plier and pulling.
Get the right size tap to repair the threads or get new nuts (!) from a vendor here.

Here, what they look like after coming loose; is it even possible to replace them in new condition? If doable I'll look for some good ones

Agree if not cross threaded, they should work.

I didn't realize you still had the cages. Rgalla is right...easy to replace the nuts inside if cross threaded. The cages just squeeze into place

I got a set of new cage nuts. I'm trying to do the ends by the doors first' but, I haven't had any luck squeezing the flanges so the cage fits.

Is there a trick to this ?

Assuming the cage is the right width for the hole, the easiest way I've found is to hook one side of the flange into the opening...then push on the other side to compress it as you push up and snap the other side in

I removed mine from the inner dash before I had that repainted.
Then just replaced them....no issues at all.
Should be doable.