J, most 'open delta' welding transformers are nothing more than two single-phase welding transformers wired together... with one leg of each going to one phase, and the remaining leg of each going to separates. While they're running at a 120 degree (rather than 180) interval, the output result is not substantially different enough to negate performance.
When you drive across the two, you'll be effectively driving a high-voltage winding.
If you attempt to wire them in parallel, you MAY find that it's particular about phasing, ie. it will work fine with one of the transformer primaries flipped, but not 'normal', etc... and this is simply because the transformers' secondaries are probably tied together at the rectifier stack, rather than driving diodes independantly.
I've had plenty of Airco enthusiasts message success stories to me of theirs, so would NOT be surprised if yours does too.