It seems like pilots' intuitions are a very sharp source of info sometimes.
I've been working for EVA for almost two and a half years and all I can say for a guy in a situation like yours is stay where you are, unless you are unemployed and without any nice perspectives ahead of you.
Facts and figures:
Typhoon is right: SIC time is worthless here in the US. Forget this 'heavy iron' thing... this is blah-blah-blah... when it comes down to landing a nice job what you really need is PIC time, some jet time preferrably, a good attitude and some luck throughout the selection process. Flying 744/MD11 SIC won't add anything to your resume, so if you really want to differentiate yourself, continue on your left seat there at the CRJ... I am flying right seat at EVA and I would not hesitate to swap positions with you...
Being a SIC in Asia is not as bad as people say. Specially in Taiwan. A lot of their captains are unexperienced, but humble and very respectful guys and you will get a fair treatment and most of the times a good CRM, pleasant cockpit environment and, just like anywhere else, some jerks on your way here and there. Many of the captains are expats, lots of nice people from all over the world.
This is not the problem. The real problems in EVA are (1) the very intense, regrettably ingrained fear and punishment corporate culture. The crew morale is very low because most of the pilots are always afraid of getting punished for something... decision making for the EVA pilots, rather than a normal part of a pilot's life, is here seen as a complex process in which there's a great chance of not pleasing the company and therefore getting punished. This is awful. The airplanes are equipped with those snitchy FDIS systems and everyone here feels like they're part of one of those TV Reality shows... specially the locals, who have nowhere else to go and a slave-type 15-year training bond!!! The company says the FDIS is not meant for punishing pilots, but the fact is that whenever a rough landing happens, or some deviation from the SOP is detected by the FDIS, both pilots are sent back to the sim... as if a pilot could learn how to land a plane in the sim... as awkward as this might seem, it is a fact. Draw your own conclusions over this;
and (2) Schedule: it sucks. In the MD, it is unbearable. 35 ON/14 OFF, but it takes you roughly 2 days to get in/out of the island, so your real days off are more like 10-11. If you're married or somehow engaged, kids etc., think well before coming here. It seems like you can handle it the first year, but further down the road you see what a mistake it is to be so much time away from home. If you go to the 74, the situation is a little better, you usually fly 23-28 days, but you only get around 8-10 days off, and considering the time it takes to get there...
Training: it is very serious and keeps you very sharp, although within the punishment/fear cultural environment...
Pay: pay is not bad,considering the industry levels nowadays. As a 744 or MD11 FO you can expect to make 3,750 net based on 50-hrs. It is very common to hit the 90-95 hr mark, which can boost your income to around 5,300 plus per diem. Per diem is at $3/hour trip time (from signing in for a flight to returning to home). That takes you to somewhere around 600-1200/month. You also get up to 200 bucks/month for medical (even though you do get coverage by their excelent public health system there at Taiwan). You also get a 13th salary bonus every year (about $2,5k).
Interview and selection: go to willflyforfood.cc I posted a summary there of what the selection process looks like.
Bottom line: if you're flying PIC jet, continue there as it will be a lot better for you down the road. As Typhoon said, SIC time won't do you any good. If you've been furloughed and can't get a decent job anywhere else, it might be an option...
Good luck on your decision!