I have used both 2x3 and 2 1/2x2 1/2 (?) . I fit the 2x3 through the floor, and the second go around was a street car that I used the square tubing to go flush with the floor pan and cut it to weld onto and overlap the rear subframe by about five or six inches. Ditto on the front. It hangs down that one inch below the level of the sub frames, but it is very strong that way and doesn't intrude on the rear floor pan and ruin the appearance inside the car. I tapered the front overlap for looks. With the overlap on each sub of about six inch front and a bit more out back, it should be very rigid. If you feel it needs to tie into the floor pan, that could be easily done with a little sheet metal welded to the pan and tube.
Another trick is to weld 1/8 inch plate to the subframes (all four corners in front of the rear wheels, behind the front wheels) and to the inside of the rocker panels, tying three sides together at each point. That really stiffens up the whole chassis. I ran the Dart that way in the low tens for years, no problems with a tubbed rear.