Oh man! That would be a nucking nantastic adventure! If you go, I want to see a write-up and pictures!
I hiked that
section of the JMT last June, with a side trip up to the summit of Split Mtn. If you went in March or April, I think you would have a fantastic time on the west side of the Sierra crest. I don't recall anything steep in that section of the JMT, and the Split Mtn slope is simply a steady slope. The slope steepens once you get to the saddle, but it seems like you could ascend the slope on skis with lots of diagonal zig-zagging. You would encounter a much steeper slope descending the east side to Red Lake.
The biggest worry I would have are the major stream crossings, but you could stay on the east side of the major drainage, since some hikers even do that in the early summer.