There's no way to sugar coat it - I'd have given up on it by now!
How many loops are out and bunched up?
It doesn't look like winding loose wire back onto the spool is a practical proposition.
Your only hope is to separate out the loops of escaped wire, cut off the excess and join the ends - any mistakes will cross-couple sections of winding - if you even have continuity through the coil, you could end up with a section of winding shorting round in a loop.
Must admit; I'd bite my lip on the sentimental bit, and buy another to nick parts from.
There's two loops on it and that's it, that's and the two original ends.
So cut them if it comes to it, sand off the insulation and solder them back together?
I'd be game for buying another one if need be. I'd figure maybe just another small electro magnet similar to this one maybe as a part?