Which Shecter would be helpful. Cold sweat in the neck will give you that fluid Petrucci sort of tone (obviously coupled with a ridiculously good legato ad alternate picking technique). The Miracle Man is good for Thrash and high gain shred lead. However, looking at your list of influences this isn't what you are after, as you're more rock than metal. Something like a Rebel Yell set (the neck pickup is the same as in a Cold Sweat set) could be the way to go, plenty of grunt in a classic yet modern sounding pickup, that's great in mahogany guitars.
If you decide that you do want a higher gain sound, then a miracle man or nailbomb at the bridge and a cold sweat at the neck is a good setup.
