@HVYMETALDRVR
I can't comment much on Qatar, but I've a couple of friends at Emirates and Etihad. Such is the aviation cycle, it seems like Etihad is currently the better prospect. Far shorter command time (2-3 years), and I think the pay is slightly higher. The benefits are pretty similar, but I would prefer to live in Dubai than Abu Dhabi.
Emirates seems to be very short of crew and are losing plenty of guys heading home, so guys aren't able to get all of their leave each year, and the rosters sound nothing short of brutal.
With all that in mind, remember that a few years ago, the reverse was true.
I think with your 4000hrs and 2000 jet, you'll meet the Etihad minimums, but Emirates require you to have 2000 on jets >50t. I understand that they're still pretty hard on that, but the requirements do change.
You won't get A380 without a decent amount of Airbus time, so yes, you'll go straight on to the A330 or 777. Last time I looked, the 330 was the roughest fleet to be on, but with the carrot of the A380 after a little while. I'm not sure what the situation is now, however.