I think it looks good, but to center it you also need to check the "really move the window's x" and "really move the window's y" boxes (just set it to 0 offset from the center)
To execute different actions when hitting the shortcut multiple times you'd need to use the "Cycle though multiple actions" meta action and move your move&resize action into that.
One last question, is there a way for BTT to remember all set window position and sizes so I don't have to manually arrange them each time I reconnect screens or reboot?
You can try the "save/restore specific window layout" action. It uses many heuristics and can not work across different spaces due to API limitations of macOS - but it might still be helpful