My car came with an amp and upgraded speakers. There is a subwoofer box that is unsecured in the cargo area, that takes up too much space.

Mtld83 on reddit is convincing me to go for a JBL Stadium BassHub. YouTube video showing BassHub innards, showing a downward firing configuration. More reddit comments. 2addicts.com thread.

The volume in the spare tire can be slightly larger than under a single seat. Also, it's easier to clean under the seat without a box. Also, no impact to foot space. Tools that go in the spare tire volume can be placed elsewhere under the cargo space floor. However, my spare rim is 4“ wide and is dished outwards so the inside height is maybe 2”. The JBL Stadium BassHub height is 6.5“.

I could then get an underseat subwoofer, but I'm still interested in having a round spare tire subwoofer even if I place it under the seat.

The price for a new JBL Stadium BassHub has dropped as low as $300. A cheaper alternative that isn't as tall: a Bose subwoofer that comes preinstalled on a variety of vehicles. Available used on ebay for as low as $40. People upgrading sell theirs. These Bose subwoofers are actually pretty good. See How loud is the Bose subwoofer? Dakoustics on YouTube.

Add pillow stuffing to subwoofer enclosures to make the bass sound fuller (without the air-knocking sound as pressure waves bounce off walls of enclosure). See mazda247.com forum.