My son-in-law has a somewhat similar setup with in-ceiling speakers. First, he drastically improved his sound by upgrading to much better in-ceiling speakers. In a very large room, in-ceiling speakers may not sound as good as efficient, box speakers.
His small subwoofer (maybe 8-10 inch) attaches to a wall. The enclosure is quite small and not a box. This is one possible solution. I suspect it is used by individuals who use mid-scale in-ceiling speakers. The enclosure is round and on a pedestal that attaches to the wall.
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The above picture should be a circle that is connected to the base. The uploading software removes the spaces necessary for proper viewing.
Another alternative would be to get a reasonable size subwoofer in a proper enclosure that can be brought out and connected when you watch movies, etc. In a somewhat similar manner, I do this with indoor/outdoor JBL 6.5 inch speakers that usually are the rear channels on a 5.1 system but are occasionally connected outdoors when we are on the deck outside our house.