I can help with this, after 5 years of swaybacked medium-wide quarter pony.
Ultimately I ended up with a custom ordered Stubben 1894 31cm, but depending on the specs you need you might be able to find a used one close to budget. Mine fits without the need for shims or special pads, but it has larger rear panels.
Prior to that, I had good luck with older (due to budget) Prestiges, a Top and a 2000D - but avoid the foam paneled ones. Other saddles recommended to me by fitters, but that I didn’t have a chance to try, would be Jaguar, Roosli, Dominus, all possibilities. Frank Baines was also suggested but I never did find one even remotely close to my budget at the time, which was around yours.
Just as an example, there is a Prestige Top 18" 33cm on ebay right now: https://www.ebay.com/itm/204395830832
It doesn’t say whether it’s wool or foam, but just based on the panel depth as best I can tell there’s a pretty good chance it’s wool.