Redwelter, when I restored my '36 Chevy pickup in the early 70's after running it as a rat rod, I totally disassembled it down to the last little piece. At that time I welded the frame-cross member joints and replaced the loose rivets.
So far no problem with the welds that were made using an AC buzz box stick machine and 6013 rods. As for damaging the value of the truck, I drove it from Southern California to the 1976 VCCA national meet in Colorado Springs, camping along the way on the desert and in the rocky mountains. In the judging I won first in class T-2 (1929-36 commercial vehicles)against the trailer queens that never touched an actual road surface. The judges crawled all over and under the vehicles being judged and nobody noticed the welds nor other non-stock items like modern tie rod ends on the tie rod and on my home made drag link.
The trucks were probably originally riveted because arc welding was very crude then and covered electrodes didn't exist. When I was a kid, one of the neighbors was a welder and he told me how difficult it was to use bare stick welding electrodes and what a mess the welds were.
Does your '34 have the original 3-speed transmission?