FINALLY. Official confirmation that I should send in my PS4. Bummed I have to do it, but oh well. I'll try to survive while it's gone. (Though I was hoping a software patch would have worked.)

^This is the fix

Exactly! Although the total turn off thing works temporarily, if your probllem is the eject screw fit loose, it will come back. But, at least for me, as soon as I tightned that screw it never happened again (it's been some 3 months).

I don't know if they don't tight it properly on factory or if it gets loose when the console is moved around (in shipping) as it's not ever supposed to be super tight, but anyway, apparently the screw being loose mess up with the disc bay sensor. I believe that make it "think" there's a disc inside you're trying to manually eject, hence it keeps spitting out discs or trying to eject a non-present disc.

PS: In case you don't know what screw we're talking about you can see it on PS4's manual, search for manually eject disc, the screw is under the same cover you open to change the hard drive. You'll need a phillips screwdriver to tighten it, but thankly you won't need to open anything further to fix the problem, so it doesn't mess with warrant.

Even better is it's not consistent at all. I had it happen months ago, maybe 5-6 times over a few weeks, didn't matter if I was actually playing a disc game or not. But it hasn't happened since and I have been playing multiple disc games fairly often.