Danny is correct and Lou is way off base. You can switch between neck profiles, scale lengths, etc. all day long with no negative affect on your playing. I switch between Gibson and Fender in the same set often times. Too me switching from a Les Paul to an SG is harder than from an LP to a Strat. To use my played out tool analogy, that's like saying your tool box should just have 6 Phillips head screwdrivers but no wrenches, flat heads, etc.
I try to be sure when I buy a guitar it is giving me something tonally that my others do not. Having a half dozen Les Paul's would do nothing for me. So back to your question. Not sure who told you that Fender's don't work for Rock, but if anything I'd go for the exact opposite of what I already have.
You have a dual humbucker, 24.75" scale, set neck guitar with a FR bridge. In that situation I'd be looking for a Fender scale guitar with a bolt-on neck, single coils and a hard tail bridge. It's all about tonal diversity man.
That being said I'd probably get a slightly used Fender Standard Tele for $300 - $350 or a Squier Classic Vibe. If you do want to stick with a humbucker, set neck type guitar this is the best bang for the buck in your price range I think.
New it is $500, but you can find used ones in perfect shape for $400 or less.
http://www.musiciansfriend.com/guitars/prs-se-245-standard-electric-guitar