I'd suggest changing your floor plane to a cube and making sure it has a box collider. I've often seen items fall through planes. But the fact you are getting a different result in the editor to a stand-alone build is very strange indeed.

I managed to fix it. I still don't quite know why it does that or why what I did fixed it, but I'm glad it did.

For the objects that were parented, I had to reparent them (often that meant moving them out of their parent in the hierarchy, recreating the parent, then putting them back in) and for the objects that did not have a parent, I simply had to recreate them. Most objects needed to be "re-done" one way or another as said above, but some didn't and I am still confused as to why.

To anyone who comes across this issue, keep your parenting structures simple and if anything disappears upon building, recreate it and it should work fine. Duplicating it via Control-D or Command-D does not work. You must create a new object from scratch. It seems as though some objects had some kind of invisible property that made them uninstantiable when built. This would explain why duplicating them didn't fix it (the property got copied as well, but a new object didn't have this property.)

I am 99% certain it wasn't anything visible in the editor. I've checked all components the troublesome objects had and nearly all settings in each similar component. Some objects didn't have scripts, so I didn't check those thoroughly.

To the developers of Unity, you've created something incredible. Incredibly powerful, versatile, and ingenious, yet also incredibly confusing at times. You'll get it right, I know you will ;)

Check your game object tag. It should not be editor only