1:1 backed-up, dual-handled ascenders on the primary climbing line, 2:1 friction hitch on the other. You fashion the hitch when you get up there, though.
It's for positioning, and for working the other stem, and back and forth between them as you'll need to do maybe a few times.
You have now rigged a double rope system, (DRT) where one of the ropes you're climbing 1:1 (1:1 DbdRT) and you intend to incorporate a hitch into the second climb line (2:1 DbdRT). What you will have is a
DRT, DdRT, DbRT setup,
all at the same time.
And you rock, Bob. It's two-fer Tuesday at your favorite radio station and they're dishin out some Clapton and some Skynyrd and all kinda good music to see you through the next
2-1/2 hours, you got in a groove. You didn't forget anything and you didn't drop anything critical. You just had a fabulous afternoon, and found it novel that you took your 2:1 hitch, anchored one end to the tree at the tie-in point and worked SRT off of it for awhile (DRT, 1:1 DbdRT, SRT) and at the end of the climb, you de-anchor your SRT line after attaching 1:1 midline, disconnect ascenders from the 1:1 ascendered line, abseil out on the single doubled line (1:1 DbdRT)
You mix it up. I would LOVE to have a day like Bob just had.