Hello Will:
The proper foundation in a basement is at least a 1' square cut out in the floor, dug down to undisturbed earth (which you should reach in 1' or less) then poured with concrete to the top (flush with the floor). While the concrete is still wet you could take a 16d nail and cut a 1/2" deep groove around the foundation which you can fill with silicone caulk later.
An L shaped bolt could be put in the center and extending 3" above the floor as soon as the concrete is placed. That bolt would give you something to keep the posts centered; you could even drill a 1-1/2" hole through the post centered at 3" up the post for access to the end of the bolt and giving room for a washer and a nut to hold the post securely.
Glenn
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