Adding a sub to modest system

This SVS SB-1000 should fit the bill!
https://www.svsound.com/products/sb-1000

I found a great REL sub at The Music Room. They also helped a friend of mine decide what size sub he needed. In other words, they're very helpful and have great deals on a variety of different brands (what they sell varies and they only take in good quality stuff). I would suggest you contact them and start a conversation. They have a 14 day trial period and all gear is checked out in advance. I do not work for them, I swear! I just find them almost unique in terms of great deals, variety of gear, helpful customer service, and a return policy.

Any one sub will make a nice improvement. What you will find however is it will sound a lot different depending on where you put it. All rooms have an inherent tendency to bass reinforcement and it varies a bit room to room but the overall pattern or tendency is always there regardless. This makes it so you have to move the sub around playing with location and levels and EQ trying to find the one best compromise. 

This is really no different than what you went through with your speakers, the way the tone and bass response changes with positioning relative to the walls and your sweet spot. Main difference is with bass the sub does not have to be equidistant like is so critical to stereo imaging. 

This is the basic idea behind a distributed bass array or DBA. That since no matter where you put a sub it produces a bass hump somewhere, then put several subs in several different locations and the combined result will be smooth bass. 

So add your sub and experiment and learn. Keeping in the back of your mind however good it is, it will be even better with more subs. What you will find, four cheap subs will work better than one, every time. The beauty of it being you can get one now and add later, winding up with killer state of the art bass. Or you can get four really cheap ones now for whatever you are planning to spend and have bass that is not quite SOTA but way better for the money than you could get from just one. Or anything in between. This is after all bass we're talking about. More is just about always better.

Here are my thoughts of things to consider:
https://speakermakersjourney.blogspot.com/2020/04/how-to-not-buy-subwoofer.html

Great advice, thanks

I use a small Sunfire SDS8 in my office setup at work, and have been happy with it. Can be found under $300 on amazon. Is it as good as my Rel’s at home? No, but I don’t expect it to be. It fills out the lower registers adequately for a workplace environment where by definition I am not rocking out. It only specs down to 32db, and that shows in performance, but again, I’m trying to balance getting decent bass performance using small bookshelf speakers (Spendor, Kef, NHT rotation) without being asked by building management to take the sub home because annoying neighbor tenants -- so far, so good. My amps that I’ve used it with are Bluesound Powernode 2 and (soon, waiting to receive) marantz pm7000n, both of which are in the same ballpark as your yamaha. The SDS10 and SDS12 are not too much more $$$ usually, depending on how much space or how big your room is.

FWIW, I previously tried Monoprice’s low-cost 12" 150W (around $100-150, varies) sub that gets some good ultra budget shootout reviews (I forget the model number) but both times I owned it, it developed a humming noise that I couldn’t stand. Returned the first one for replacement, and even the replacement suffered from same problem, so I returned as well for refund. There are lots of other user reviews stating same.

If your budget is really low, I can also recommend the Acoustic Audio by Goldwood PSW12 for around $150, which I have in my secondary (bedroom) HT setup at home (replaced the Monoprice for me). It has been solid for HT and also for music (2.1ch) for when I was streaming music there before upgrading on music (still use it for HT). At these prices as long as they don’t hum (really important), and then can produce decent bass without sounding too boomy, it’s a win.

Probably the $500 SVS or Rel will beat what I’m discussing here I’d guess, but everyone’s budget is different.

Of course one could make a great case that now would be THE time to look seriously at room at acoustics.