Since the riveted joints are stress risers, stitch welds will crack. If you decide to weld these joints you would probably want to make the joints extra strong with gussets and added steel plates and continuous welds. If the final build is much heavier than the original car then there will be greater flexing. Cornering at 70mph and having your frame come unglued would be very embarrassing.
If the rivets are all tight I would leave the frame alone with what you are doing to it. Be sure to check the rivets though, particularly the small ones on the bottom of the front cross member. Use a screw driver or pry bar to try and separate the joined pieces of metal. You will most likely find some that are broken but both ends are still in the frame. In my opinion, re-riveting is not a good option. The factory rivets were done with a machine that made sure the two pieces to be joined were pressed very tightly together but even the rivets have their drawbacks, even from the factory. If the holes aren't exactly lined up then the rivet will get formed into the hole but with an offset. This offset creates a square edge in the internal shank that is prone to crack and break, particularly on the small diameter ones. If broken rivets are found I would probably fully weld the cross member(s) and do regular inspections on them.
The Jalopy Journal
