I'm only commenting to express my interest in this as well. I've been working with the table for 3 hours now and don't see a way to do it (i'm still very new to TTS though, so there's that).

I found a solution in the meantime. You can edit your save file TS_Save_X.json (where X is the number of the save slot you are looking to make changes in … better make a backup copy in case anything goes wrong); search for "Nickname": "Flex Table Control", and make adjustments in that JSON object, for example the Transform & ColorDiffuse objects. You need to reload the save in order to see those edits.

OH! i figured out of to move the button to a different leg. In scripting menu there's a "location.self" value about 1/3 of the way down that is default set to leg4. I changed mine to leg 1, and then applied a scale and it moved.

the issue then is that it opens in the same direction, but if you have the menu open you can edit the rotation value by using the "move" tool on the left side menu and clicking in the scale value field. It should bring up the normal menu that has the scale, position, and rotation values, just edit the middle rotation value in 90 degree intervals until it's facing the right way.