Look at the tread wear. At 4,600 miles I would say its time for some fresh meat back there as opposed to dropping more than 1/2 the $$$ for a new tire in a tire well past 1/2 of its life. Fixing it doesnt mean much patching. You could do it yourself. Get a new tube & put a patch( the best ones have a rubber "titty" with an aluminum cap wrapped around it, to make shoving it thru the hole possible. Once its in place, the aluminum comes off & the rubber gets cut off even with the surface of the tire.The patch is just to protect the tube from some little something hitting the hole the nail made. Wont protect near as well as a new tire would, but if it was a new tire, Id do it.

A come along & a piece of rope will get that thing off the ground, if you have an overhead joist or limb that will handle it. Quick, cheap & easy. How you tie on matters, or it will lean over.

If that idea bothers you, 2 pieces of 2X4, a chunk of 4X4 or 2 short pieces of 2X4 stuck together & a piece of rope to tie the 2X's together makes a quick, easy bead breaker. Lay the wheel on one 2X, run a loop of rope around the end poking out, lay the chunk on the tire & , stand the other 2X on edge, run it thru the rope loop, adjusted so the boards start crushing down on the chunk laying on the tire so that it doesnt drive it into the rim, but down on the tire. Everything is still usable as boards & rope, except for the little block, so it really costs about nothing.
The "Ride it on flats" idea is something Id try, next time. What could be easier? But I rode a flat rear for a ways & it didnt come off the rim, but it was a pretty new tire. Maybe with some wear it would work out. IDK if Id drop the thing or not, but I can see this being an easy something to try.

Ive had to work pretty hard to get the rear to break loose. I dont think my knees are heavy enough. Maybe I could get Atlas to come by & kneel on it..

Any preference on tires amongst the people on here? My front has got some dry rot & I don't feel comfortable with it, the back can probably wait, but I need to do the front ASAP  

Nail two 3' 2x8s together, add a handle, and you have a bike lift to go under the frame under the engine.  Jack up the rear and you have the rear ready to remove the wheel.  The routine is in the Clymer manual.
http://www.myacrobatpdf.com/2122/suzuki-ls-650-savage-86-a-04---service-manua...  There's some fiddling around to find the nuts for the belt guard, but it all goes off and back on easily.  In any case, those prices are way too high...find a different shop.  My local shop mounts a tire for $21; you do the removal and reinstall.

I just put Pirelli MT66 Route tires on my Savage and like them a lot.  The 140/90-15 fits the rear.  I bought a new rear tube with a 90° valve stem for easier inflation checks.

We dont have a car with a bumper, its all plastic bodywork now. Ill just do my 2X4 trick, like I posted. But, If I still had one, Id give that a try.