Dear Shane, I've seen your request merely by chance. Hope it's not too late. Please note, that if you're not into watch repair, don't even try to do it by yourself. The westminster clocks contain 3 very powerful springs. For an unexperienced person, their dismantle or disassembly may appear dangerous.
On the other hand, don't take anything for granted from the sayings of the watch-repair shops. Believe me, I've been into this business. Don't just give your precious clock to anybody's repair.
As a matter of fact, most likely, that this problem is easily repaired. Many times because of "over" winding, the central circle of the spring coil slightly widenes and the slot jumps out from it's hold to the Spring axis. From this point, the attempts to wind it again will look exactly loke you have described. An experienced person can dismantle the coil casing, open it, and slightly tighten the central coil circle. That's all to it...
Another minor problem that may be there: the outside pinion that holds the spring casing from turning, is damaged. Easy to check visually...
Other possibilities: The Spring may be broken, Some teeth may have been damaged by the spring casing...
Anywhay, it sould not be too expensive to repair.
Good luck.
Edward Oded Yudovin, January 2009