Thank you everybody for chiming in!
The Devine RX-10SA looks nice, but I can't find any measurements. I'd rather not buy blind if possible.
BK Electronics looks great. I'd have to ship them to Switzerland though, at which point they are way over budget. I could order two Speedwoofer 10Es for the price of one XXLS400. So, sadly that's not an option.
Buying used is an option. The used market is quite good here for the products that are available here.
A car subwoofer is a creative idea. I'd prefer a more living-room-friendly design. The car subwoofer would have to outperform the other options substantially for me to consider that solution.
Velodyne prices seem to be high. The cheapest I could find quickly was around €850.
The Adam T10S looks good. Again, I can't really find measurements though. Going by
@sweetchaos's subwoofer comparison list.
Crossover, phase, and room correction are in place. I am using Audiolense for that on my HTPC. The subwoofer will be connected to my RME AIO Pro.
I probably don't understand
@sweetchaos's subwoofer comparison chart properly. I thought that a linear output from 20Hz to 125Hz would be ideal. The more volume the better, but for my room, that is not a main concern.
Going by that, the Kali WS6.2 is at 96.6 (-6) at 25Hz. It doesn't go lower than that. That's pretty good. The Speedwoofer 10 has 101.1 at 25 Hz, and 93.7 at 20Hz. That sounds a bit better to me. How much difference will it make in a small room with crossover and dsp in place?
Thank you again everybody for your help. I appreciate it.