Hi OP
l would stick with Rel as you are there already to go with the dialling in with your pre use qualifications. No need for apps, just a good pair of ears.
Go for a T7i or T9i second hand. Both have 10” drivers, the higher the number the greater the amplifier power. No point in paying for a new X model in those sizes, there was no discernible difference to my ears. You may find a stereo pair would fit in your budget if used ones are abundant. They both have high level Speakon and low level RCA inputs. Rel developed this first and l advise you do not accept other brands that do not offer this. High level for Stereo and low level for those extra channels for home theatre…..it’s a no brainier with total flexibility. Rel may only go down to 30 Hz but l never found this a problem, my neighbours yes. Also don’t go for extra large drivers as your bass can end up boomy and bloomy. Smaller drivers are quicker and slicker.
l use two Rel T9i subs and as a guide, l bought second hand for £650 and £550 (roughly $1500) in the UK. One would be enough but two for me are best as you don’t have to drive a single sub so hard. Less chance of a bake off frying incident. You will take a risk of course with no warranty, but the choice is yours.