With a year left on my contract, would the Army Reserves be willing to work with me in letting me out early or transfer to IRR status?

Depending on where you are abroad you might still be able to serve your last year. Look into reserve opportunities in or near where you might be working as well as look into IMA positions that's individual mobilization augmente. If IMA you could get your last good year in completed in like a month or so and be free except for your SGLI debt

It is up to your Bn, Brigade and USARC. My friend, an Officer, had to nag his unit and his RSC for 9 months with calls, e-mails and face-to-face conversations to get in the IRR. You may have to do the same. He was talking to and e-mailing the Commanders and the civilians. It was painful. Good thing the USAR and civilian staff are not affected by the partial gov. Shutdown.

IRR is an option but it would depend on the command, they may request a letter explaining the reason and it also depends on the command, some commands are more willing than others to work with soldiers. As the LTC mentioned there are reserve units overseas, you could look into that.