Among more modern lenses, something like an earlier Symmar of around 360mm ought to do well and fit your price range. 360mm may seem short for a portrait lens, but I rather like it, and it's been a fairly common focal length for 8x10" portraits historically. Another good possibility might be a 14" Commercial Ektar (Karsh used one), which will be in an Ilex shutter with bipost sync.
If you don't have a lot of extension, the 360/5.5 Tele-Arton will cover 8x10" at portrait distances, but not at infinity. I have one, but I find it a little too clinical for portraits.
Veritos are usually in studio shutters, so you would have to add sync to them, but they are beautiful portrait lenses. The 360 Heliar is usually in barrel, but it's another favorite of mine. Generally, anything that is 360 or longer/f:4.0 or 4.5--i.e., most of the classic portrait lenses--is going to be in a primitive shutter.