Subs or Turntable?

You don't need an amp with an additional set of outputs to use speaker level inputs on a sub. You just connect the sub's wires in parallel to the speaker cables at the amplifier or speaker binding posts.
 

I’m aware of that. I was explaining why I couldn’t use subs that do NOT have a speaker level input because my amp does not have additional inputs. 

I vote for subs first. And with that, I suggest you consider a distributed bass array. Look at James Romeyn for example. I’m not saying get it. It may not fit your style. But use it to think about the cost/value of subs in their different implementations.

I have heard two systems that leveraged a swarm/DBA set up, and I was very impressed with both of them. But given the size of the room and the need for the room to continue to feel comfortable (as requested by my wife), I don’t think this configuration would be a good fit at this time. Maybe someday in the future I could experiment with it, but the layout would make it extremely difficult in this room.