Whatever brand you decide and especially because you’re using the sub for 2-channel music I’d recommend getting two subs. You could get two SVS SB2000 Pro subs for under $2k that will get you down to 19Hz (-3dB) and would be good for both music and movies. They also come with an app that allows you to dial in the subs from the listening chair using your phone, and they offer a risk free, 45-day trial including shipping both ways, which is also nice. Not too familiar with REL subs but not sure you’ll get down to 20Hz with them at your price point if that’s a concern. Best of luck.
https://www.svsound.com/products/sb-2000-pro