Update time...
On Saturday there, I got out the welder and decided to give it a try...
Bear in mind that the garage is attached to the house, the bike is currently resting on bits of wood, on top of a tarp, which is in turn on top of a couple of layers of carpet. Also bear in mind that I liberally doused the engine in degreaser on Friday night to get rid of most of the 14 years of muck!!
I managed to get a nice arc going, but I couldn't for the life of me get the nut to properly attach itself to the stud. I was just creating a small ball of weld on the end!! Turns out welding is hard....
....Starting a fire isn't so hard though.

one of the errant sparks jumped onto a rag which I had used to wipe off the degreaser the day before... oops! Cue me jumping about the garage like an idiot to get it put out.

Only burnt through the tarp and one layer of carpet, so it's ok..
Put the welder back on the shelf at this point and got the dremel out. Following the advice on here, I took off a couple of mm from around both studs. The lower stud came out fine with some heat and one of those halfords stud removers. The top one ended up needing an old 7mm socket to be hammered onto it. Once it was on nice and tight it came out fine. Phew!
Now to dig out the old copper washers and get the rest of the bike in order!!
