A complete bagger system from Deere is $350. Is the entire system toast, or do you just need bags and a tube? New seat $30 )eBay Motors), ignition switch $7 (Advance Auto Parts).

From what you describe I would fix it.

Yes, i think, if it runs ok, then fix it. The Dealer, of course, wants you to buy a new one! Isn't that why they are dealers?
The parts you describe are not that expensive. As for more power--whut? Are you going to race with the neighbors? I've had lawn tractors that had 14 hp or more, and after i installed a used 12 h.p. engine, to replace a blown one, the tractor did the same thing it did when the original owner had it--namely, cut grass, towed a cart, all the things you would normally use it for.
As for the larger rear tires--well, the larger the wheels, the lower the power from the wheels.
Back in the days of steam engines on the rail-roads, the engines that hauled passengers had large driving wheels, to allow the engine to run at higher speeds, without over revving all of that massive machinery! but, the engines that pulled long lines of freight cars, had smaller drive wheels, to transmit more power to the drive wheels, but not as much speed.
So, to me, it would seem the higher h.p. would be discounted by the use of larger wheels.