If you don't see the difference between trying to get hired at Delta vs getting hired at Spirit then you are just kidding yourself. You can get hired at the airlines you listed as an FO at any regional you think of. There are pilots at Spirit actively applying to Delta... that should tell you something. Go to a job fair and watch the lines for the different majors. You are going to see people congregate on the larger, more stable airlines. Look at the hours of those who got hired at those airlines. If you want any of the airlines you listed then go right ahead but those are risky airlines.

I really like Alaskan but you still aren't getting hired there unless you know someone or have a ton of time. If everyone is getting hired with the magic 1000TPIC then why are there so many guys stuck at different regionals twiddling their thumbs. When Delta, United, American, etc start hiring... the competitive minimums will be pretty high. Do you want to rack up 7000 hours scraping by living in a rental apartment or do you want to have a life and be able to go on vacation. Thats the difference between great lakes and a larger regional. Neither is pretty but there is a better QOL at one.

There are no shortcuts unless you are exceptionally lucky. You are gambling that you wont be stuck at great lakes, that they stay in business, and that nothing happens to you that ruins your chance at a major. The 3 that went to Alaskan were the exception and not the rule.