If there are any Guitar Center locations within a reasonable distance, there's a chance they might carry an Aerodyne in the store. Plus, they have a very generous return period…45 days, I believe. Plus, you can order something off their used database, have it shipped to a store location
(if you don't want it sitting outside your home, waiting for Bob-Knows-Who to take it off your hands) where you can give it a proper shakedown trial. If you like it, you're done. If not, you can return it right there, on the spot and no questions asked. The only thing you'll be out is the shipping fee, which usually amounts to $20 or so.
A used Geddy-sig or Aerodyne might be a bit over your budget, but you may end up getting a free bag or case along with it. That being said, either of those might fit the bill. From many, many accounts, the Geddy's have some of the thinnest, front-to-back Jazz necks around. I believe the thinnest ones are the Japanese-made models, the USA model has the thickest and the MIM's seem to fall in-between the two.
Aerodyne necks are neither super-thick, nor pencil-thin, but their fretboards are a bit curvier. Dunno if that's a deal-breaker or not, but there you go. Their P/J pickup configuration…or for that matter, any other P/J…might be up your alley. You tend to get a bit more "thickness" in their sound, but with a bit of "growl" from the bridge pickup.
Just out of curiosity, not to mention the possibility of "compatibility", what model Squier have you been rockin'? Things like series
(Affinity, Vintage Modified, etc…), model, year and country-of-origin can determine whether or not a replacement neck is a viable solution. For example, if it's a late-nineties/early-2000's, Indonesian-made Squier Standard, you might run into compatibility problems.
It's worth mentioning that I have a couple of parts-basses that I might be parting out soon
(re: the link in my signature below) and both of them have excellent, Squier Classic Vibe necks. But then, almost everything that came out of the CV series was very, very good.