I play nothing but fretless and the best buy I have seen in years is the Squier VM series. You can get either the Jazz or Precision fretless, or with your budget, both.
Guitar Center has a few of the VM Jazz basses on the website used for $199. They are almost always in pretty much mint condition, because unless you make fretless a life choice, you're probably not going to play it that much.
Nice thing about the VM series in general is that all standard parts fit them, so if you want to upgrade the perfectly good pickups already in them, or anything else, it generally tends to be very plug and play.
I prefer the Squiers to the Fender MIM/MIJ/MIA fretlesses for one major reason: the fingerboard. The Squiers have ebonol fingerboards (a composite), same thing you'd find on a Pedulla, Status, Steinberger or any other high-end fretless. It's ideal. Hard as nails, I've played nothing but rounds on my Steinberger fretless for over thirty years now and I've got some minor scuff marks. That's it.
If you just don't do Fenders, I'm a big fan of the Cort B4FL, which is a great bass (I have four) and I'm seeing a brand new one on Reverb for $479 right now. Free shipping. The Ibanez Portamento series is made by the same people and they've got some nifty offerings. Both the Cort and Portamento basses are unlined, which, if you have not played fretless much before, might be a bit offputting.
Also should mention the MTD basses, very reasonable and if they made an unlined version I'd own a few of them. They don't, but they make a nice fretless, albeit with lines.
Really good time to be a fretless player. Most manufacturers are offering one, and with the exception of the Rogue MF/GC housebrand, which is awful, almost all of them are perfectly decent, playable instruments that will last for decades.
One major problem is that you're looking for a fretless fiver. Not many of those out there, not cheap ones anyway. Someone's got a fretless five Status in the classifieds for $1600 but that isn't cheap by any standards and it's way over your budget. My advice is go with a four and drop it to BEAD tuning, which is what I ended up doing.