I agree. The 90 degree column is the wrong place to look for your ampacity, but it's a very common mistake.
You are limited by the temperature ratings of the lugs at the ends of the cable (see 110.14C). In every installation that I have ever seen or done you ended up being limited to the 75 degree column for the ampacity.
350 kcmil THHN is 310 Amps.
8 sets gets you 2,480 Amps.
Since the overall ampacity is greater than 800 Amps, you can't get any relief from 240.4C.