Lots of good advice in this thread. I figure I'll add mine because, well, it's PoA and beating the same topic over and over again is what we do.
One thing that I wanted to say is that it's likely your idea of a 'good' QOL will change as you get older. I'm guessing it's pretty wide right now (which is a good thing!), and will get narrower as you age and assume responsibility to more than just yourself. You're young, and I don't say that in a condescending way, but just to emphasize that the things important to you now will almost certainly change in the next decade. You admit that you have SJS, and you know what? That's fine. You
will eventually learn that the novelty of the airplane wears off in a matter of months, leaving your happiness tied to the realities of the job itself. But that's not something you'll understand until you experience it - no amount of us telling you this will change your mind. The good news is that you're young and single, so it's far better to learn this lesson now, rather than when your QOL affects more than just you.
As far as your actual decision, I don't think either path is a
bad choice. The 340 will be a ton of fun, some great experience, and I'm sure it'll be far more memorable than simply instructing for another couple of months and hopping over to the regionals. And there's a lot of value in that - there's truth in the old adage about the journey being more important than the destination.
Trouble is, when the destination is the airlines, it's risky to d!ck around too much with the journey. Especially when the hiring wave is going on *right now*. I flew 340s and 421s for a couple of years, and it was the most challenging and rewarding flying I've done in my career. Problem is, the computers don't care, and the computers are the gatekeepers to an airline interview. Once you're in the interview, that 340 time might help when a human is talking to you face to face, but the interview isn't the hard part -
getting the interview is (I'm talking about the majors here). And that computer that's pulling your resume from a stack of thousands doesn't see a 340 any differently than a Seminole.
So when it comes to getting on a seniority list of a major as quickly as possible, I think the safest decision is to just instruct to 1500 and jump to the regional of your choice. Once you're there, keep checking boxes for the computers. Upgrade and get TPIC as soon as you can. Become a check airman as soon as you can. Go to job fairs. Keep your nose clean. Apply apply apply. Delta might be your first choice, but cast a wide net, and make decisions on where to work once you have the job in hand. Your Dad will obviously be a huge asset here as well.
I really want to tell you to go have fun in the 340 - that's kind of the path I took, and I wouldn't trade those experiences for anything. I did a lot of things flying corporate and charter that I'll
never experience at my airline. But that also happened in a time where the 121 world was stagnant, and my detours didn't hurt my overall career progression all that much. Yeah, there are fantastic corporate jobs out there - some even as good as the legacy jobs - but based on what I've seen on this board, I think even if you
had that job, you'd always be looking over the fence at your Dad and his 777. That's my impression at least. And if that's really what you want to do - go get it. You're in a good position to do so, or at least as good a position as you can be. Just stay focused, and keep checking boxes for the damned computers.