Engineer has some steep switchbacks on the Silverton side. Not sure of your preference, but with the big bike I like going down them. So, from Silverton you can take Cinnamon Pass to Lake City, then Engineer back over.
I gotta admit that in 6 years riding an 1150GS I never took it over Engineer. Do-able for sure as I had been over Ophir and Cinnamon numerous times with the GS.
There is a stretch of Engineer that you will definitely want to stay off. The portion that connects US550 from closer to Ouray. Big rocks, steep switchbacks. The best way is from Silverton through Animas Forks(cool ghost town).
There are so many passes that don't get the 'big names' (Engineer, Black Bear) but are just as fun and scenic. For instance--Bolam Pass, Last Dollar Road, etc.