I’m mostly welding large hoppers and chutes made of 16 gauge stainless steel. We are required to fuse the outside, but add 1/16 to 1/8 welds on the inside. The most aggravating part is that we’re not allowed to use purge systems and the bends/size of the pieces make the use of backing impractical or downright impossible. I bent the rules and made a little purge block out of scrap but I got in trouble for “wasting gas” when I was caught using it.
I’ve had a little luck running at 30-40amps with 045 wire, but not much.
I’m hoping somebody has some thoughts as to what I can do to weld 16 gauge without backing or purging.

Thats a tough spot to be in.

Perhaps backing the weld with some aluminum foil and tape could keep most of the oxygen out. How much post weld finishing is typically done on these parts? Sugaring isn't just cosmetic, it comprises the strength too.

I think Brian has a solid point - as disheartening as it may sound see if you can find a shop that shares your quality values, so you can feel good about what you make when it goes out the door. I'm lucky, I work for an outfit that does not accept second best and it really helps your morale.

Yeah that's really difficult. Maybe if you use machine pulse with laywire and thick filler you can reduce burn through, trying to get the filler to take most of the heat. I don't really like welding that way and sometimes it's difficult getting the filler to wet out rather than ball up, but we also have thin sheet stainless products at wok where minimal burn through is desired. Pulsing helps me a lot with heat control.
As a guideline if I do an autogenous outside corner on 1,5 mm stainless, which I think is the same as 16ga, I will pulse at about 40 amps peak current, 2pps, background current as low as possible, peak time and background time equal to each other. Without foot pedal. A nice clean electrode grind is necessary to help arc remain stable during background pulse