In a rush to remove the starter (did my clutch) I failed to remove the signal wire bolt from it so when I pulled it out it broke in a not so great place.

I happen to be really good at soldering do you think there's anyway to salvage this mess? Maybe try to solder the wire back to the mount and shove it back in there. Or should I just give in and go to pull a part (or worse the parts store) for a new solenoid?

If I really wanted to save it I'd probably just cut the wire and hard solder the S.O.B straight to the lead coming out and heat shrink it

 

You will need to pull the starter, and then see if you can use a large gauge jumper wire.
But I think you will find a swap would probably be best solution.

You can often just get the solenoid, but up to you, that would depend on the age of the starter motor, if it is over 10 years old I would just replace the whole unit.