highly specific cat peeing question

I've scanned the last 18 months of posts to no avail, and so I turn to you, HDers, with a highly specific question.

About two months ago, my partner and I adopted a former stray cat who's about a year old. She is pretty laid back but, being young, needs to play a lot. So we play with her. Right now she is deeply in love with the plastic ring from a milk jug. She brings it to us in her mouth, we throw it, and she plays fetch. We do this until she flops out. It is highly entertaining.

Problem is, twice in the last couple of weeks she has wanted to play at 2, 3, 4am. She leaps onto the bed, drops the ring on my partner's chest, and meows. We attempt to continue sleeping, or pet her ears and turn over. 15 seconds later, we realize SHE IS PEEING ON US. OK, the comforter or blanket over our feet. BUT STILL. HORROR.

We have had her health checked out. It is great! Top notch!

We are adept with Nature's Miracle and laundry tips. Thanks, HD archives!

Her box is scrupulously clean, and we take special pains to scoop it before bed.

The obvious answer is to shut the cat out of the bedroom, but then we're worried she will start peeing in other areas that we won't find until later. My partner works from home, and between the bed episodes, the cat peed in the hallway, in view of him, when he was on a call and couldn't play. How much do we need to wear out this little creature?? Do we need another cat or will that just double our nightmare?

Our vet is talking to us Thursday, but I am praying some of you have also dealt with this issue successfully. Thank you!