Subwoofer - is there one that would work in this situation?

I was wondering if that would be the case

I just read the measurements in Stereophile. This is a speaker which you want to put a DSP crossover in front of your amp. You need to tame it’s peaky behavior around 70 Hz and the location of your sub will also cause you some further issues.

A DSP crossover, set to HP at 80 Hz And smooth out the bass peak + the appropriate EQ for the subwoofer is going to be your best bet. Of course, it’s a difficult location. Try the AM Acoustics room mode simulator to give you the best places to put your speakers and sub.

I’d forego doing this at all unless you put an EQ in front of your amp.  that peak will make it much harder to integrate well with a sub, but.... and this is key, rooms turn all bass specs into a hot mess, so measurement first is going to save you.

Kef KC62 might be just what you're looking for. 

In-wall or in-ceiling subwoofer...

A Norwegian company called Sigberg Audio makes a very high quality and very slim subwoofer called the "Inkognito" which is designed to fit behind or underneath furniture, and would probably work great on a shelf below a TV. 

No affiliation.

Duke