Get the 1000 hrs TPIC. Then look at the horizon - with 1000 hrs TPIC you might already be in the top 10% of candidates. What's the next biggest resumer fluff you can get? Part 121 CKA would be GREAT. That's not on the horizon? I'd chase a LCC and get more experience on a larger jet and a new type rating. That job can also be a 'destination job.' Keep you foot on the gas until you get to your final 'destination' job. I'd recommend pressing on to a Big 3 job for the option of doing w/b flying. Most try and those that can hold it with decent seniority often stay on it for years. Some guys do it for their entire career. It has i'ts downside (less seniority and sleep cycle issues) but the most common advice is "it's a different airline." It's LIGHT YEARS different than doing domestic n/b flying. Reread the comment about guys who NEVER do domestic n/b flying. Or the guys who take the Captain upgrade but say they're going w/b Captain as soon as they can. Former FO, who didn't care for 767 w/b flying, is chomping at the bit to give the 787 a shot. At worst he'll have two years on it and he can bid back. If he decides he likes it he's on the best fleet doing the best flying in the industry.
You're 27? So at least 2,000 hrs at a minimum. At least one type rating. At worst you'll be 30 w/3,000-4,000 hrs and 500-1000 hrs TPIC. That's a top 10% candidate on paper. They want to meet you to see if the candidate they see on paper is the individual that walks in the door.
If you got hired by AA at 28, based on today's data, you'd retire as #143. Hired on your 29th birthday? #256. Hired at 30? #385. 31? 515. Delta and United might have similar projections. Is one of the Big 3 within driving distance? That's your career goal.
Good luck.