In today's smaller, over-worked, and transforming Army, there are always options for a soldier with a good service record.
I believe Cliff R gave some sound advice...talk to your Bn or Bde career counselor or retention NCOIC/OIC. They should be able to point you in the right direction. If you were within one year of your ETS date, you could probably re-up for it, but since you have a few years left, that limits your options. You could always try to see if a guard unit in the area where you want to work needs your MOS also. If they do, I think it is possible to make the switch, but it takes a lot of coordination between the gaining and losing commanders.
The only other thing I can think of is emploring your chain-of-command to consider an early termination of your current service obligation, based on a considerable life-style change which could result from getting this job. I've heard of soldiers who have won lotteries or other-wise inherited large sums of money and been able to get out. I know in order to do this, you have to be able to provide bonafide documentaton that the new job (or inheritance)will dramatically enhance your lively-hood somehow. Then it really is up to the losing command. Example: A soldier at Ft. Bragg won the McDonalds Monopoly game, back in '97 or '98, when I was stationed there with the 82nd Abn Div. He was able to prove to the Div Cdr that inheriting close to $1,000,000 was a significant life-style change, which the Army couldn't begin to compete with, so they let him go.
If your unit is expecting to deploy to OIF, OEF, or the Balkans anytime soon though, I wouldn't get my hopes up. Likewise, you claim your MOS in "non-essential".... You may think this to be true, but in these times of war, EVER soldier is important in some way. If your departure from the unit would create a vaccuum or leave the unit under-manned somehow, then you can forget making the switch unless you have a very benevolent Bde Cdr.
Best of luck. At the very worst, maybe you could ask the potential employer to hold the spot open until you are eligible to get out.....they would gain a more seasoned and experienced leader in the long run. If you aren't already an E5 or E6, you would probably be one by then and would have some better schooling under your belt for the resume. Best of luck.
DD