This shouldn't be the end of the world. The stock shielded twisted pair will work fine in terms of current. Just run the first run from the filament DC supply to one tube, connecting the shield at the lower hole of the center terminal on the closest 5 lug terminal strip. Run the second run to the other tube, connecting the shield at that tube's closest 5-lug terminal strip.
If you get tempted to use heavier gauge wire, you may end up with shielded twisted pair that is stranded, and that can make a huge mess in a hurry.
-Paul