What would you do if Delta’s answer had been “don’t ever apply here again”? If Delta had told you that, would you take the other major job, or stay at your 135?
If you’d take the other major job in that scenario, then I would suggest it might be a good idea to take the major job in the scenario you currently find yourself, because there is no guarantee that Delta will hire you on your second attempt.
Personally, I’d take the major job, and then interview at Delta again in 6 months. Second interview success rate is quite high at Delta, but still not guaranteed. However, you know exactly when that 6 months will end, and can spend the last month or so prepping heavily for a second interview.
Bottom line: if your career stalled, where would you rather be six months from now, the major, or your 135 operation?