Yer on the right track Tom
The Custom has a fairly thin profile compared to many. The Classic is a tad more beefy by comparison --not a bad thing depending on what you're looking for but I definitely wanted thinner, which the set-neck on the Custom allows.
I tried a lot of 5ers in the $500-600 range (Ibby, Yamaha, Schecter, etc) and the Peavey Millenium was the closest in feel to the Spector in the neck (and no offence to the the Peavey players but the I thought the Legend Custom had it beat for quality and attention to detail and worth the extra $).
In fact, I bought the Custom for the neck and the string spacing. Lord knows I'm still not reconciled to that gold hardware
See my post here for a pic of the Custom showing the neck, though it does not show the profile it will give you some idea
http://www.talkbass.com/forum/showthread.php?p=5640416&highlight=custom#post5640416
By the way, the set-up on this bass was great out of the box. Low and nearly even. The set neck scares some people off, though it does have a truss rod, I have not had to tweak it. I like the stock strings too, which I believe are made by GHS.
Good luck.
And let us know how you make out.