I think you're over-thinking this. You need one queen, not 100, right? So look for a frame with eggs in your queen-right hive, and put it in your queen-less hive, normal orientation. The bees will take it from there.
I'd wait about 4 weeks before disturbing them after that. Let them make a queen cell - you don't want to damage any queen cells by manipulating the frames too early - and let her emerge and mate and start laying so she's established before poking around.

I'd wait about 4 weeks before disturbing them after that. Let them make a queen cell - you don't want to damage any queen cells by manipulating the frames too early - and let her emerge and mate and start laying so she's established before poking around.