At 1,500 hours, you're not going to stand out.

Turbine time is good, and pilot in command time is good. Where ever you go, you're looking for entry-level positions, so keep that in mind.

The brief hiring bubble has deflated with a whimper. Legacy carriers are pausing hiring. The freight titans are at a standstill.

If I understand your post correctly, you've been flight instructing for three years, and feel it's time to move on. Fair enough; most don't instruct that long, any more, though there's nothing wrong with teaching. Someone above mentioned going to Arizona to instruct. There are schools there that do volume instruction with foreign students.

We do what we must, in our careers. If the job you want isn't hiring, find a job that is hiring, and go there. Many jobs aren't glorious, but it's a career, not a video game. Go fly the Grand Canyon. When you get a few more hours, USA Jet is looking for 727 first officers. Charter operations all over the country are hiring. If you don't want to instruct, then tow banners, fly skydivers, do aerial survey or powerline or pipeline patrol.

Single engine turbine is turbine, but not really multi turbine. It's good experience, though, as is anything you approach with a professional attitude toward your flying. One thing I see a lot of first officers show up without, is PIC experience. Gain all you can. Look for that first multi job. It may or may not be in turbine equipment.

Flight instructing isn't glamorous, but it's useful experience, and most of the captains in professional cockpits hold or have held instructor qualifications at some point or another. Many of us still maintain our CFI (etc). At this stage in your career, avoid tunnel vision; it's a broad industry with a lot of kinds of flying, including airline flying, but by far not exclusive to it. Don't overlook the myriad opportunities that abound. Subscribe to a few of the job listing sites (planejobs, climbto350, usajobs, jsfirm, etc) and get a feel for what's being advertised. Over the course of my career, I've flown air ambulance, sprayed fields, fought fires, towed banners, instructed, flown grand canyon tours, flown jumpers, worked for the government, flown in garden spots like Iraq and Afghanistan, surveyed wildlife, done aerial photography, performed atmospheric research, flown fractional, charter, and corporate, as well as airline flying from passengers to international freight, and a few other things along the way. There's a lot to do out there, and if you don't like what you're doing, then find something you do like, or that helps you meet your goals. It sounds like your goals involve primarily multi-engine flying, so put that on the shopping list. If you can go fly a Caravan or PC-12, do that, too. Don't overlook ACMI flying. Consider the FAA. Consider the military. Think about fractional and corporate. Regionals are a far cry from what they used to be, and chances are that you'll never endure the kind of pay and effort that many of us were required to expend, to get established in our careers: you may not realize how good you have it, regardless of whether the temporary hiring bubble has slowed or not. Jumping to an ultra-low cost carrier may not be possible from your present position, or even from the single turbine (but it also may). You have opportunities and time. Don't limit either one. It's a lifetime journey, and it doesn't need to be completed tomorrow.