I did exactly that on a '70 that I owned way back when. I made it longer than the door openning so that it stretched from behind the quarter panel side to side, bolted it to the quarter panel on each side with a round headed bolt, ran the body mounts through it down to the rear frame member and made a sheet metal lip to merge the floor with the new cross piece. It was stronger than the original for a fraction of the cost and all that looked out of place were the two round headed bolts--painted nicely. Now if you can weld it in all the better!
I saw a vehicle that used a standard tubing size - I think it was 3" x 5" x 1/8". The extra width makes it easy to tie into the existing floorpan. It also gives you plenty of surface area for the body mounts. One note, make it as long as you can, you may be able to reach the rear outer body mounts if the existing channels are in bad shape.
I haven't done this myself, so take my opinion for what it's worth. "A bird in the hand is worth what it will bring".