Yes, we did circumnavigate the lake.Lucky you I did the SC a couple of years ago and the road round the lake was still snowed in. It was a late snow year, I was unable to cross Elk Pass south of Mt Rainier either. Moral of story: check with the relevant authority for pass snow conditions if it's before August.
Someone in Ashland who had done it told me you needed a mountain bike to do the Windigo Pass Alternate. From the above comments it looks like she was correct. Actually the reason I didn't try it myself was hunger: adding another pass sounded attractive but I thought i stood a better chance of getting food in Chemult than anywhere on the Alternate route. A cafe shown on the ACA map on 97 that I was counting on for breakfast turned out to be closed.