Can I enter into the IRR?

Being allowed to submit for IRR and actually getting an IRR transfer executed are two very different things.

One can always go to the IRR. By contractual obligation is the easiest. Otherwise you could submit a request for an exceptional situation (which never gets approved)

I would first start off by trying to find a new unit. That in itself might be enough to make your life easier, but you need to do your research. Getting in a non RFX unit is the biggest start.

Another tactic is getting transferred into a unit from where an IRR transfer is possible.

#1 does the unit actually action personnel requests in a timely manner
#2 does the unit execute IRR request when the IRR window opens per the contract. I've seen IRR requests sit in limbo and the soldier just ETS's based on the hard contract date.
#3 does the IRR approval authority approve IRR's that are outside of contractual guidelines.

*****
Honestly, I was in your situation and slammed by the USAR. It was just very clear this couldn't work in the long run, and I needed to divest myself of association to the USAR. I was an RFX Commander.

Then 27 months time in command I simply transferred and poof, the only thing I've really done that took any time outside of the actual Battle Assembly was put together one training brief. Oh, I can totally do this long run. I can certainly even give more. I just can't be at the whims of the USAR every single day and night, especially unpaid, and no travel coverage.

I think you should start there. Look for a new unit.

It is every Reservist's right (especially lower enlisted) to find themselves in a situation of 1 BA a month 2 week AT a year and nothing more (with a training calendar that doesn't change 2 or 3 times a year). Just like the advertisements IMPLY!!!

When I was in the reserves many many years ago, I had to provide a letter from my employer stating that work would conflict with drills for me to be put into IRR status.

SSG Wes, you should look into some government contracting jobs. I'm not sure how it works but I know your Reserves time would be put on hold. I've worked with many guys that were in Reserve units and did contracting for a number of years, and when they went home (when they were done) they just made up their time. Could be an option for you but the money is really good.