Ah, the OP asks for sub recommendations and it sparks the age old debate of if you “can” do home theater and 2 channel listening in the same space, shared equipment. Before I get to that.
I’ve got an REL sub, 2 SVS subs. I was surprised at how well the SVS keeps up with the REL in 2 channel. I can’t comment on Rythmik, but sounds like either will be a winner with Rythmik a better fit for music. I would say the SVS subs totally outshine the REL in HT performance, that’s to be expected though as the REL is designed for 2 channel listening.
On one of the age old debates… if you have a nice set of speakers, subs that work well with both music and HT, absolutely you can have a great set up for both. Is there truth in an AVR receiver not holding up to a stand alone 2 channel amp, yes there is. To get the best out of 2 channel adding an integrated or pre amp / amp with HT Bypass solves that issue. The extra amp for 2 channel will in most cases improve HT performance if using an AVR Receiver to power all channels.
That all said, are there potential trade offs if you have your system in a space that shares the space and the majority of the equipment for both HT and 2 channel, sure. You might lose out on speaker placement flexibility, component placement, length of cables, speaker wire, room treatment and have a limit on the overall budget (money). All those are legit points made by 2 channel purists and 2 channel will be more affected by the above.
Done right you can have a great, I mean great set up for both, in the same space. And a great HT set up is night and day to any 2 channel set up for movies, despite what some might say.
It comes down to priorities and how important both are to you. Will your 2 channel be the harder of the 2 to dial in and could sharing the space make it harder to squeeze the last little bit of goodness out of your space, equipment, that is legit.