Whitefish - Logan Pass ride

I’m heading to Whitefish, MT for a wedding next week and will be bringing my bike. I’d love to ride up Going To The Sun Road to Logan Pass beginning in Whitefish. I know that cyclists are only allowed on that road prior to 11am or after 4pm and this route round trip is roughly 130 miles. Ideally I’d be leaving Whitefish around 5:30-6:00am and getting to the base of the climb around 8:30-9:00am.

Has anyone ever rode around this area done something similar to this or even ride up to Logan Pass? Any advice or feedback?

Epic climb. Watch for bears. No joke.