Some brilliant suggestions so far. I need to try a So Cal out as that is pretty much the right style but it is the higher end of what I want to pay, if I can find a decent super stray type with a big neck for a couple of hundred then even better.
Checking out Schecter now but it is difficult to tell which one have bigger necks, must measure my DGT as that is the right sort of shape. Sambora strat would also be purfect but pretty hard to find a mex one at the moment!
+1 for the Schecter. ESP LTD have some nice necks, too, a nice U shape, but not as skinny as a JEM neck. Also worth hunting for a nice USA Wolfgang - they're beautiful to play, though I don't get on with them.
Discontinued but still quite a few used examples around.
I have a a HSS Stagemaster which I picked up for <£100 on eBay and I'm actually quite fond of it. Basically it's a reversed headstock strat with the body mildly reshaped behind the neck heel for easier access to the higher frets, a Floyd, and a bridge humbucker, very much an EVH "Frankenstein" style hot rodded strat rather than a purpose build shred weapon and as such the neck profile is more Strat than Shred.
A mate of mine used to have one of those Washburn super Strats (Mercury series?) and that had a neck profile like a 50's Les Paul. Could be just what you're looking for. I've not looked but I'd imagine you'd find one on e-Bay easily enough.