Hi Dan
The Ibanez Artcores
are your best bet in that price range. The pickups are a bit too "Gibsony" to get the Gretsch sound, but that's fixable with a set of TV Jones or even some of the Budget GFS Retrotron range. The tremolo tailpiece you are looking for is a Bigsby, BTW.
Finally, how would a semi-hollow body hold up using overdrive or distortion? I've heard that thinner bodies produce less feedback, but should distortion be avoided all together when playing on a hollow body?
Ted Nugent does OK with a Byrdland at insane levels and lots of overdrive. Generally, the deeper the body the more resonant it will be, the more resonance, the more chance of feedback. The thinner bodies often have ES335 style centreblocks which make them more stable too. However - part of the Rockabilly and Rock 'n Roll sound is a full, deep hollowbody (with a slapback echo). Fortunately it's not a loud or high gain style of music, so even these guitars are manageable.