Thomann makes a fretless Violin bass [url="https://www.thomann.de/gb/harley_benton_beatbass_fl_vs_vintage_series.htm"]clone[/url]. If you want something cheap and easily returnable to try it out first,
Did you get a short scale model made then? Because I'm close to your height (about 3/4¨ shorter) and a 34" scale P bass neck looks longer on me than that Wal's does on you.
Eastwood makes a copy of the original Ampeg fretless bass that would be in your price range
https://www.eastwoodguitars.com/collections/bass/products/eub-1