Just some basic info for you if you are not already aware.
The Classic shares the same swingarm and bevel box with the Standard, Classic, Classic Tourer, and Roadster. It is made to have a 240/50-16 stock tire on back. Some Captains have been able to fit a 245/50 with just a bit of clearance. Of course, many of us run car tires in this arrangement with no issues.
The Touring model has a different swingarm and bevel box and is sized for a 180 series tire. I don't know the exact size offhand.
You "best" option, if money and skills allow, is to convert to a chain/belt system if you are truly after the insanely wide tire out back.
Otherwise, imho, you should look to the Standard swingarms.