You're not going to a major with that resume. Frontier and Spirit hired some guys in the <2000 hrs range. Especially not as the hiring demand eases right now. If you do you'd be a unicorn in a field of 5 leaf clovers. "Five leaf clovers? I've never heard of that." Exactly. That's the same with a 1500 hr CFI going to a major airline today. Has it happened in the past? Absolutely. Don't use that as your career path. Busting you butt flying at a regional is the best experience you can get to prepare for a major airline job.

Get to a regional and start busting your ass flying. Oh, they get you that ATP. Get better at that job. Learn. Watch the experienced guys. Ask questions. Realize that not all of the answers/explainations are solid. Figuring that out is also important. "Show me" is a great question. What's the book say? What's the training guidance?

A Citation is a nice jet but it's closer to a C-172 than an airliner in a lot of ways. Wing loading? C-172's probably 13.8 lbs per sq ft? Piper Arrow? You know the dreaded 'high performance' rating? Noticeable different sink rate, power/drag, etc, on final? It's 16 lbs/sq ft. Citation? As low as 44 lbs/sq ft. Fighters? The 'high wing loading' beasts??? About 90 lbs sq/ft. 737-800? It's 129 lbs/sq ft. 777-300 is 165 lbs sq/ft. There's a big difference going from a SEL to a turboprop to a small/light jet to an airliner. W/b airliner has some differences again but it's relatively smaller than the first steps.