Sub Confusion

"My goal is not more base- I’m looking to free my PMCs from having to expend energy to produce sound below 80 Hz and increase depth."

To do that you will need a sub with a high pass filter. You need to use a separate amp and preamp or an integrated with preamp out and amp in!

If you use Rel subwoofers, those don’t have high pass filters!

What Yogiboy said. Adding subs doesn't automatically make life easier for your other components. I think your speakers are transmission line designs. Removing sub-80Hz signals will mess them up. You need to rethink what you're trying to do. 

As mentioned, the 212/sx is designed to run in tandem with your main speakers (no high pass).

Generally, stereo subs would be preferable. That said, i have a single 212/se in my system and don't want for anything below 80hz, so there is always more than one path to satisfaction.

I agree with just about everyone’s posts. That said, 80Hz high pass might be a bit high for your speakers considering they can dig down to 26Hz. If your goal with subs is to clear up the frequency spectrum and deepen the soundstage, you likely want them performing largely below audible frequencies and will want two or more in the room.

Even without a high pass, you will be surprised what two good subs crossed over at 65Hz or lower will do to the rest of the spectrum and to the sound stage. Should you still want to combine this with a high pass for your speakers, I suggest looking first at a 60Hz high pass as 80Hz may be too high.

While the Rel 212 is a wonderful sub, it is a lot of a single sub for that room. The others you mention though do not dig deep enough. I would probably opt for two 812’s, and if that’s too much money, the SVS SB-4000 is a worthy competitor at a fraction of the price and offers better integration with its mobile app.

In full disclosure I run a hifi business but do not carry Rel or SVS. 

"SVS SB-4000 is a worthy competitor at a fraction of the price and offers better integration with its mobile app."

Ummmm do SVS subs connect via the main amps outputs? I dont think so. the above statement will never be true, just because theres an APP? Thats not how subs integrate.

The REL subs connect through the main amplifiers outputs just like the main speakers for true integration and you dont do this using Hpass filters either!

If you need more than one sub your using the wrong subwoofer.

And to answer the OP's question YES the S510 will be plenty for your room size. I would buy it in a heartbeat. And make sure you set it up as REL reccomends for best bass response and musicality......YES REL's do more than produce bass they are musical and when tuned in properly they make the main speakers come alive even more and allow them to play with more detail and ease. REL subs sound beautiful.

Thanks

Matt M