The NEC allows for downsizing of wire to welders because they are not a continuous load. Wire size is determined by amp draw and duty cycle. You can run a 50 amp welder on 12 ga wire so long as the duty cycle is 20% or less.

Edit to add:
As we add 50A 220v outlets around the farm, we are installing the 14-50 since it is a 4-wire connector. We have an adapter from the 14-50P to the 6-50R with the H-H-G connected (N not used). This allows a camper to be plugged in when friends visit and also allows us to easily add 3 20A 120V circuits since we have a fuse box that plugs into the 14-50 and had 3 20A fused 120V duplex circuits in it. The OP could easily make an adapter with a 14-30P and a 6-50R to adapt the welder and just not use the ground pin.

(wire_ampacity (full).JPG)

(duty_cycle (full).JPG)

(6-50r (full).JPG)

(14-50r (full).JPG)

wire_ampacity (full).JPG (79KB - 72 downloads)

duty_cycle (full).JPG (41KB - 68 downloads)

6-50r (full).JPG (12KB - 69 downloads)

14-50r (full).JPG (8KB - 68 downloads)