Update on my subwoofer journey. I ended up just buying a Dayton audio Sub-1200 as many initially recommended. Got a restocked unit for under a 100.00 shipped, so we'll below my initial 300.00 budget. Did a sub crawl and made a minor adjustment to the setup. Recently had purchased a newer AVR, Pioneer with Advanced MCACC. Ran the calibration and Pro EQ. It set the Sub-1200 at +1 with the gain at 12:00. MCACC set everything else, LCR, around -5 dB. Strangely enough, the old Jensen I've been using for 15+ years suddenly sounded like pure garbage. I set it on top of the Dayton and switched back and forth between the two. No contest.I'm afraid you have some competing needs; $300 budget, large space, quality bass. Large space is fixed and can't be changed so it will have to be one of the other two items where a compromise is made. Depending upon your definition of "quality" that might be the easiest to forgo; considering what you've been using any of the $300 subs would be an improvement, so in that regard you almost can't go wrong.
While I agree with the others - DIY can be an excellent way to drive value into your system - in the budget subwoofer category that's a bit more difficult. Let's say you want to spend the same $300 you would on a commercial product. For that you have to buy a driver, amplifier and all the building materials. I suspect it would be quite challenging to get all the necessary components for $300. A few hundred watt amplifier alone would be half or more of that budget, if you want to get something of reasonable quality of course. Then there's the protection mechanisms; you would be responsible for creating them so you have to factor that in as well (low cost drivers aren't robust enough to handle much abuse so it would be unwise not to have pretty strict filters setup).
If you don't want to get an off-the-shelf product head on over to the DIY forum that bargugl linked, it couldn't hurt to ask the question and see what they say. There are some very talented people in that section of the forum, but don't be surprised if the $300 cap causes problems with their recommendations too.
I'm very pleased and haven't even finished break-in. Watched Day after Tomorrow Monday night at just below reference level and had to turn the gain down a little bit. I have determined I can't push it very hard or it starts to get distorted, but with it nearly at my feet, setting it low is not problem. Very pleased with my sub 100.00 purchase ( pun intended).
This should satisfy my bass head urges for a while. Maybe post Covid I'll find a Speedwoofer, Rythmik, or HSU deal and trade up. But very pleased, especially for the tiny investment.
Thank you @JimWilson and @Deaf-Forever and @bargugl for all your assistance, as well as anyone else I missed.