Check with FedEx, too if you don't mind flying cargo. They're not hiring now. But they soon will, I hear.
If you had, supposedly, less experience (and therefore less perks to lose than now) and joined a US legacy airline, say in 2013, you would definitely gain seniority faster that a decade ago, due to the mandatory retirements starting to kick in next year.
In UAL, there's 11,000 active pilots and the projected retirements until year 2031 will be 9,900 pilots (by taking into account a base scenario of no furloughs due to the economy and fleet growth at 0%).
In any case, if you stay put, because of your credentials and the flexibility in bidding they come with, a good approach would be ten or nine months of active rostering with consecutive bids until building a monthly average of 78-83 hours (one favorite example: KIAD - RJAA (14H15'), 24 hrs layover, RJAA - KIAD (12H15') x 3 = 79 hours - actual duty time on the flight deck is a third of that approximately). That gets you 19-20 consecutive days off a month. And then two or three months in reserve. But I'm sure you've already been doing something along those lines anyway.
Good luck in whatever course of action you choose. Whatever makes you happy!