ahah, chicken strips! I never managed to clean them off either bike on the street. I's so NOt worth the risk of wrecking a big bike like the busa. If you're up North like me, forget it. 5 months of good riding, dusty roads in Spring, potholes and gravel chunks throughout the Summer, by the time things start to look relatively safe and you're getting into your groove, winter is about to set in again. HAHA, glad to know another rider who will admit to getting over 3000 miles out of a rear tire!! I once got 10k!!! Past the wear bars to the bottom of the tread but still!! I usually get about 6-7k and I think keeping a front on there double time is prudent economy but if it's a few years old might be best to change it along with the rear unless you are going to just do straight touring miles with the bike until the next tire change. The rubber gets hard and it's more important to have grip in your front tire than your rear.
I mounted my last set of tires myself. The rear wheel is not too difficult. The front requires almost twice as much force. Balancing is easy to do but IMHO, not an absolute must on a motorcycle (you're already getting 7000 miles out of a tire, FCOL!). You can pick up a balancing stand for about $100 or less so it's a good thing to do just to be sure you did a 100% job. If you do this yourself, buy the right tools and prepare to set aside an entire day the first time you do the job. Last thing you want is to mar up your rims or scrape a bead surface. Tire changing with irons requires a lot more force than any other wrenching I have done. The OEM rims are very strong though...I don't think it would be likely they could bend from tire changing but you will wonder as your prying down on a couple 15" irons. You also will have tires on your hands now that you may have to pay a fee to dispose of at the local dump.
Far as letting a shop do it, find a good one that will assure you they won't let your rims get scraped. Mine were scraped by the dealership shop the first time i changed tires. They will get it done quickly however and dispose of your tires for a small fee (unless you let them do the whole job of removing and installing wheels) + they can get the tires you want for a 10 dollars more than you find online (unless you come across a great deal online). If you don't change tires often, doing it yourself isn't economical. If you take a lot of satisfaction in doing your own wrenching, GO FOR IT!
Here's my tutorial I wrote for the Gen1 ZX-14. Same applies to the busa or any other sportbike tire. Refer to the busa service Manual for removal and installation of wheels.
Tire Removal and Mount
BTW, since you plan to keep the old front on there, why not try something different than OEM on the rear? The front is not going to have optimum grip anyway since it is an old tire. I'd try a 190/55/17 on the rear for a few mm of lift. I like that on my 14 but that bike does not turn in as good as the busa. If you're staying with the old front, might not be of much use to get a real sticky rear because you prolly shouldn't be pushing your cornering with a sticky back and an old front....in which case, new OEM on the back may be best.
