There's some more tricks i should mention. Smaller rods can help, i can't remember ever going lower than a 3/32 tho, but 1/16 might help starting out. If you set it up so it's vertical, any globs will simply follow the joint to build it up. With cellulose (6010, 11) rods, you have ample penetration if you need it. But in this situation, you don't really need it at first. So your goal is to literally spatter up the gap until there's enough metal there. Once you build it up enough you simply burn it in. I was actually taught that trick with mig, when welding the cat d11 radiator guards they had a few joints that had half to 1 inch gaps.
My first day i turned wayyyyyyy down and started weaving it together. The old timer teaching me came unglued, came over, took the gun from me, cranked it wide open, and literally drug it super fast back and forth over the gap. Within moments he had enough shit built up to simply weld over it with a light whip. I was schooled right and proper. Later i learned the same trick with pipe and stick welding, which done right will pass xray no problem. Learning this technique will allow you weld on stuff smaller than the electrode, and wayyyyyyy thinner than a 6013 or something like that.
Since you have new material that can take the heat, try to favor that side. The thin stuff will burn back some (sometimes more than others), but will usually ball up a bit on the edge, which is thick enough to weld usually. If it's simply burning away too quickly move around even faster. Once again the goal isn't to weld it at first, but to literally put enough spatter on everything where you can weld it at the end. You usually have to let it cool a bit in between passes if it's glowing. Go weld elsewhere where it's cool or if need be, walk away for a few min. That's the hard part lol.
Jim, that sounds like a rough day bud, i feel for you.