Nickel is your friend! It bonds to danged near anything metalic (see Periodic Chart of Elements)..hence the 8% N of 308...better yet 309 with more nickel.
I'm not so sure about bismuth/antimony alloy (ie. Potts Metal that melts at 180F used in fire protection systems).
Now when you say rejected...Please elaborate... lack of fusion, porosity, spit fire balls atcha? etc...otherwise, did it just pile up? swiss cheese? volcano?
Clean, Clean, Clean, Clean.
"The only filler small enough to be melted in the weld"...What, ya aint got no bailing wire handy????

If You don't have any small enough welding rod or bailing wire, cut some lengths of MIG wire and use them.

Was the mild steel filler the same diameter as the stainless?

Hey Fritz

GTAW hates mill scale and corrosion of any sort when doing mild steel  (GTAW also hates un-killed steel)... If your steel wasn't perfectly clean inside and out (including root faces and sheared edges) than that tendency for boiling and popping in the puddle can haunt you.

Sometimes folks can grab gas welding wire  (R45) which looks just like regular tig wire, and make attempts at GTAW with poor results...

I prefer ER70S-6 cut lengths for GTAW on mild steel... it is high in deoxidizers which help to reduce that awful boiling and popping... Others prefer ER70S-2

I think Lawrence is on to something.

I've had several instances where RG-45 or RG-60 was mistakenly provided by the supplier when less than a full box of filler metal was ordered. To the person behind the counter ER70S-2, ER70S-3, ER70-S-6, and RG-45 all look the same. Not everyone standing behind the counter at welding suppler's store front is a welding engineer. As is the case in many companies, the counterman may not have the training or background to know all the ins and outs of filler metals. Now for the salespitch - can you say "AWS Certified Sales Representative?"

A little rust on the filler metal isn't going to be very helpful either.

I would definately start with checking the filler metal to see what type it is. Then check the condition of the metal you are welding. If it was cut on a saw that uses a liquid coolant, it has to be cleaned if you want porosity free welds.

Let us know how you make out.

Best regards - Al

Maybe not using enough deoxidizing filler metal.  Some steel puddles "boil" or out gas when welded autogenously.  Even when using an appropriate rod, not getting enough filler metal in, or not getting it in quickly enough can create the same outgassing problems, like you described.  The result being holes in the weld.

I too have seen RG accidently substituted for ER on several occaisions.  A tip off is outgassing and pinholing in the weld and/or reduced tensil strength.

Sounds like Al and Lawrence are on the right track.

Sounds like dirty material or incorrect filler. A good test is to run a bead with no filler to see if you're still getting problems which rules out base metal being an issue.  Anyways Austenitic stainless steels will except a lot more interstitials in the weld and hence can "eat" up a lot more contamination or outgassing before things showup as pinholes or slag.  Not an excuse to use dirty material and not clean, but it can make the difference between a a really difficult weld and something that doesn't take any second thought.

I would figure out what filler you were using.  I doubt they would use un-killed steel in square tubing. That stuff is usually already EB seam welded.