Why not just do the GCT and add a route down to Hetch Hetchy via Smith Meadow/Peak since you're going to be up in that trail system anyhow? The elevations in that area work in your favor.
That hike along the North Rim is also nice. If it intrigues you, give it a whirl.
As far as Ten Lakes go, Balzaccom is right, being a basin, it's going to be colder and have deeper cover. We had this report a few weeks ago from some guys that did exactly what you're wanting to:
viewtopic.php?f=7&t=3572So I was up there last weekend. What I saw from the road on the front side of the Ten Lakes trail roughly up to the pass looked clear of snow for the most part. I was at May Lake at ~9300 ft. It had a lot of deep cover, not full coverage, but enough to make it an issue on a few levels. Even looking up to Mt Hoffman above us at 10850, there was some snow, but it wasn't solid cover. Sure there might be SOME snow at 8000, but everything I saw except for deeply shaded and/or north aspects was nothing, and even in those locations, it was nothing to get hung up on or that would stop you in any way. We found no snow except intermittent patches below ~9100 in S/SW aspects. Although, what we did find was that in the heavily forested valley below the trail junction up to Tuolumne Peak @ 8750 (your exit from Ten Lakes) at the May Lake trail and down to the Murphy Creek trail junction, it was averaging maybe 3-4 feet deep over maybe 70% of the ground, obscuring a good part of the trail, and there was a lot of deep standing and flowing water from runoff on everything else, especially to the left of the trail. Murphy Creek was runoff hell, but it had been raining all day when we went through.
So, 9500 is too high, 8000 is too low, and it all boils down to aspect, if it's forested, whether it's soil or granite, if the weather cooperates, and if you have the skills and determination to get through all of it.