So there's a ton of confusing information about the IRR. Enlisted members generally have an 8 year obligation in their original contract, which means if they don't re-enlist or do SELRES for the balance of 8 cumulative years, they have to serve out that balance in the IRR. As far as officers are concerned, the information is contradictory. Some people say officers are ALWAYS at the behest of the military, meaning you're in the IRR forever by default. Others suggest they have the same 8 year threshold of combined AD/SELRES time before they're clear of the IRR. And yet, there's been stories about folks getting passed over in the IRR (everybody does effectively) and that demarcating a release from it after being twice passed over. But that would go against the idea you are forever beholden to the IRR as an officer.
In the OP's case, the situation is different because the cat got separation pay. That one is from my understanding, an additional 2 or 3 years in the IRR. My presumption being, that is on top of the 8 year original contract.
So, what to do? Resign your commission. That's where you'll have to call ARPC and will require a letter and paperwork. As opposed to what people think, a DD214 is NOT a discharge from the military, merely a release from active duty. There is a Certificate of Discharge from the US Armed Forces that actually represents the legal release from any further military obligation. Military pensioners for instance, are forever beholden to military recall, though for realistic logistical reasons are seldom invol'd.
The problem for the OP is I think they won't let you resign your commission with a balance due on IRR incurred due to accepting separation pay. Once that is done I believe you'd be allowed to resign your commission and be forever free from the military if that is your intent.
As to losing out on a trip, Jeeeeesus Jaywalking Christ man, you want fries with that too? Pull a day of mil-drop on the schedule and be done with it. SW will reshuffle ya. You're a first year guy I understand that, but you're not losing a ton of money. I understand anything is a ton of money when you're making regional pay, but you should have thought about doing your homework when it came to separating, plus you're sitting on VSP money. Sack ***up Brotato chips.
Yes, it's only 150 dollar check for muster and travel is on you, unless you're gonna claim personal hardship to get out of it or ask for a date push to the right, I suggest you just mildrop a day on the back or front end (your legal right, SW ain't gonna say **) for travel plus the muster day, and get it done. Research the resignation of commission option and exercise as soon as possible but beware, once you do that, you're done for good. No SELRES for you, ever. Last thing we indentured servants wanna hear is you coming on here whining about wanting a Reserve gig to get you through a furlough or seniority displacements due to merger/stapling 10 years down the road.
Good luck to ya.