Welcome to Glacier Park Chat! Any time you can get a night at Sperry or Granite Park Chalet's, it makes for a great hike, I think... and having one at each is all the better.
I think the estimated route you are aiming for is a great one. The hike out from Granite Park over Swiftcurrent Pass is quite nice. Did that with some friends last fall. 2 thumbs up there. And then coming into to Sperry from Gunsite Pass is also a great way to go.
Some general thoughts would be... Be prepared to get creative on your routes in case you are unable to get what you are aiming for as it's not guaranteed. Perhaps a night at the Swiftcurrent Lodge or cabins or the Many Glacier Hotel if needed. Some other options to consider as plans B, C, and D if needed might include going south west out of Granite Park down to The Loop and catching a shuttle or 2 from there. Head east over Logan Pass down to the Gunsite Pass trail head and go in there, or go west and stay at Lake McDonald Lodge and then come in from the west and still have access to SNY, SPE, and ELL before heading back to the Chalet. Just some thoughts as back up plans... I'd still aim for what you were thinking though...
Some other thoughts would be regarding Gunsite Pass. It's typically just fine but it's always a good idea to keep an eye on the amount of snow on Gunsite Pass, even late in the season. I don't believe I've used micro-spikes in that snow section though I can think of once or twice when it probably would have been a good idea. While the snow section there can be small to non-existent, it can also be quite large and the slide from there could make for a
very bad day. Anyway, that's just something to be aware of based on snow amounts and what your comfort level is. Typically it's not a problem.
All in all, I'd say you have the makings of a great trip. Perhaps others may have some other thoughts as well. Oh, and if you have time, I'd be sure to head up to Sperry Glacier while at the chalet. That's a great day hike if you can swing it. Saw my first wolverine up there too almost 10 years ago. We'll be up at Sperry again this year some friends as well the first week of September. Maybe we'll run into you.... Ya never know...
Cheers!
Kyle....