Steve,
On the first table [if I am looking at the right one], I would say that the demand on free air feeders would be only high for minute times - not exceeding an hour or so.
On the other table T430-72 (b), I have some referenced notes that came with my 99 NEC, which edits the printed text.
In that note, there's a few points towards values of 400% of 310-17's 60 degree table, plus 300% of 310-16's 60 degree table.
I'm not exactly sure what level of current would cause a #10 cu to fry, but 160 amps would be at least close enough.
Is this going in the direction you were hoping??
Scott SET