Yes Todd, the whole tire, wheel, brake, spindle and suspension contribute to undesirable unsprung weight.
I still have Michelin TRX tires. I like the wheels so I spend the premium on tires from Cooker. I just replaced them after 15 years and 50,000 miles because of all the discussion on tire age. When I got them off, there were no cracks or checking that would lead to failure but they were beginning to get worn and hard. For the price of the rear tires alone I could have bought a complete set of wheels and tires.
As for rear brake effectiveness, the rear is the first place to start to improve Tiger/Alpine braking. By replacing the poor performing rear drum brakes with proper disk brakes you then start using the rear to help stop instead of just the fronts. Because disk brakes are self-adjusting, you drastically reduce pedal travel the same time. You can then use a smaller master cylinder, eliminate the lousy booster and end up with less pedal travel then stock. You have to be concerned if you increase the front piston area too much you will affect the front-to-rear balance. Rear disk brakes are also lighter!