If the Steve Harris model is a 1.75" wide nut with a thicker profile, it is probably what Fender describes as a "Thick C" profile, such as found on the Roger Waters sig p-bass.
NOTE: This is only a guess, as Fenders site has no info on the neck profile for the SH model. I don't think Fender would make yet another thick style of the 'C' profile neck though, as production-wise it doesn't make sense. The '57 AVRI is also 1.75", but is simply (too simply) described as being "C shaped", although I think they meant "Thick C".
I tried out the '57 AVRI and the Roger Waters a few months back, and if I recall, they were the same profile.
After awhile, I found I could adapt, although I didn't buy either.
Maybe someone who actually owns a Fender with a Thick C could verify.