Take a look at the SVS SB1000 Pro. It’s a sealed basically 13” cube that’ll still get you down to an honest 20Hz (-3dB) and includes an integration software app so you can dial in the sub with your phone. The only problem is it’s only $599 so might not be expensive enough for you…heh heh.
https://www.svsound.com/products/sb-1000-pro-subwoofer
Best of luck.