Since OP is asking for a Classic & not a touring, many on here are running the Bridgestone Excedra Max 240/55R16 on the rear, paired with the shorter Avon Cobra in a 140/75R17 on the front and all are happy with that. I made that switch also & loved it. the shorter front tire makes the bike feel like a complete different bike, being easier to maneuver. The last front tire change I switched to the Michelin commander II in the 140/75R17 and after about 1500 miles I believe I actually like it better, definitely grips better in the rain and I'm judging that from having them on at last years 3 Sisters ride when it was raining the whole time on the very twisty roads there.
The Mich is a little more than the Avon but I believe it's worth it