I reconnoitered Milly's and Lucy's Foot Passes before going out over Thunder Pass and concluded that Thunder was the better bet. I didn't like the look of either of them, at all. We went over it in 1979 and there was no need for an ice axe when we did it in August. Being on a north facing slope, that could change from year to year, but this was a low snow year and I'd bet you won't need an ice axe. Do be prepared for lots of loose stuff-it's a rotten gully. But as long as you pay attention and move slow and careful, you shouldn't have much trouble. Certainly nothing like some of the stuff you did on the SHR. Side benefit: You get to go up the basin below Thunder Mtn on your approach from the unnamed 3 bayed lake. It is drop dead beautiful. One of my favorite spots. You're doing a great route. Best of luck.
Oops, I missed your follow on posts. Congrats, Dave. I'm glad it worked out for you. Beautiful country, huh?