Inside the tunnel is not a structural loaded area.
Not entirely true. The tunnel floor skin is probably lightly loaded, but the twisting of each torsion bar is taken up entirely by the torsion bar crossmember along with help from the floor skin. Note that the crossmember is made of a thicker gage metal than the floor skin...so the crossmember is taking in a large load, but it still needs the floor skin to work properly per the original design.
The floor skin surves to cap off or "Box" the "U" shaped crossmember so it can resist buckling. The two work together to distribute the twisting load of the torsion bars and spread this load out and into the unibody.
If you make a saw cut clear thru the crossmember, then raise one front tire about a foot off the floor, leaving the other 3 tires on the ground, I'll bet you'd see the saw cut in the crossmember open up.
Imagine if there was no crossmember at all, just a short piece of angle iron long enough to weld the torsion bar recepticle. The twisting of the torsion bar would twist the angle iron, which would buckle the floor skin around the pieces of angle iron; that is why mopar made the crossmember span the entire floor skin between the unibody box sections under each door.
Assume the car weighs 3200 lb, with each tire load 1/4 of that which is 800 lb; and assume the lower control arm of the front suspension is 2 foot long. The twisting moment is equal to 800 times 2 = 1600 ft lb. Thats 10 times the best you could twist a 160 ft lb torque wrench. That torsion bar crossmember/ floor skin combo is absorbing a real twisiting moment load, and it has to do it without cracking for years and years over many thousands of miles.
Welding could work, like said, photos would help make the determination, but a purist would probably replace the crossmember.
If you do weld, remember to etch prime and paint those welds real good. The weld metal will rust much quicker than surrounding metal that was not heated. I have seen unibody welds painted with spray cans that you could put your finger thru 5 years after the repairs were made.