An excerpt from another thread. This is good advice on tire changing. T
Heretic, I commend to you this how-to video (in three segments, I think; be patient and they will play in turn):
Not trying to put you down, but . . . as the Bridgestone rep says in the video, if you must struggle this hard, you should examine your technique.
From your description, sounds like you trashed your tire; no responsible shop, in my view, would send you out on such a critical component in such a questionable condition.
The "trick" in spooining the final circumference of a bead over a rim, in my view, is placing the opposite bead deep into the drop center of the rim, providing, geometrically, some "slack" permitting levering of the tire onto the rim.
Tools helping in this process may include C-clamps, or the commercial "Bead Buddy."
I'd suggest you check your rim run-out as Terry 1956 mentions; have the rim trued if necessary, replaced if damaged beyond repair. I'd bet your tire is destined for the land fill.
You may want to engage a reputable shop to mount your new tire. An expensive proposition, perhaps, but less costly than a tire and rim repair/replacement.
I respect your willingness to perform your maintenance yourself; changing a stubborn tire presents a steep learning curve, but you will acquire skills with you always.