The stubbies are Irwin brand bolt extractors.
I don't know if they'd do it either but if you don't force it and are patient they usually pull through.
You could also try this: heat up the bolt/nut juncture and soak it with penetrant, strike the bolt head several times (to break the rust and encourage penetration) andf then try using a cold chisel (held tightly with vise grips) and a BFH...if you first lightly tap a groove on the bolt head on the otside edge and then wail it on an angle that will encouage it to turn it may start to turn...I dunno it's worked for me...and yeah, 120v welders don't bite so good, eh?... PM me if you like, you could try one of those extractors if you want or I could weld on a nut for you....good luck...gotta love the torx heads eh?