I’m an old guy with a lot of experience and a memory that’s still mostly OK. 40x Whitney by five different routes. 11x Russell by three different routes. I’ve done them both the same day several times.
First, there are three possible permits for Whitney that start at Whitney Portal. It appears that you have the Whitney Trail overnight permit (part of the lottery). This allows you to climb the main Whitney trail. It is legal, but EXTREMELY IMPRACTAL, to carry all your overnight gear up the trail to the Whitney summit, descend the Mountaineers’ Route, and then camp at Iceberg Lake or UBSL. You can climb the south face of Russell from Iceberg Lake, or the east ridge of Russell from UBSL.
The Whitney Zone day use permit (also part of the lottery) allows you to go anywhere in the Whitney Zone for one day. Any peaks, any trails, anything you want to do. It is common to climb the Mountaineers’ Route and descend the main trail.
The North Fork of Lone Pine Creek permit (not part of the lottery) provides access to LBSL, UBSL, Iceberg Lake, the Mountaineers’ Route, all the technical routes on Whitney, and all the routes on Russell. This is the right permit for climbing Russell and Whitney on two different days.
I’ve only been on the north face of Whitney once. I was dayhiking Russell, Whitney, and Muir. I probably didn’t find the best way up the north face, but I climbed some crappy snow and ice and considerable rotten class 3-4 rock. It wasn’t fun. If I were linking them again, I would descend the south face of Russell, hike over the col NW of Iceberg Lake, and then ascend the Mountaineers’ Route to Whitney.
If you find yourself on the main trail with a little time to spare, take the short detour up Mt. Muir. The summit area is one of my favorite class 3 scrambles.