For best results use the low-pass RCA jacks for HT, instead of the high-pass speaker wires for music. You can actually connect it both ways at the same time. If the REL gets a signal from the RCA jacks it automatically uses that signal instead of the high-pass.
I actually think the STrata would be fine. The bass would be accurate, not just boom boom. Make the loud bangs more realistic, instead of just shaking the room.
REL does make their "Q" line of subwoofers. These are designed for HT. That said, the Q subs are still very musical for 2 channel audio as well.
You just have to decide what you care about more.
FYI, I have a REL ST sub in my main system and a Q sub in a separate HT system.