When your resizing brass is the die adjusted so it touches the shell holder if not its leaving the base of the shell expanded and will jam when the bolt slams shut.
readjust your die and re resize a shell and see if it cycles in and out freely of the chamber.
Don't go giving up just yet, I think this is an easy fix. I don't have access to my computer where I right now, and a long answer via my phone is a bit tedious. I think you've got a simple sizing issue, and we can clear that up pretty quickly. I'll be back in the office on Monday, and can get into a longer exchange then. Trust me, we can get you up and running in no time.
No problem at all, and I can appreciate the frustration. If you're already loading for a Garand and not having any issues there, that's a real good sign. Loading fro Service Rifles (ARs included) is a form of advanced handloading. Easy to run into problems here that you'll nearly never see with a bolt action.
The first thing I'd suggest is to use a case gage. This will tell you what's going on, and allow you to know what you're changing when you start trying to adjust things. Without them, you're essentially loading in the dark. I'd suggest something like the RCBS Precision Mic, but there are several different types out there. Even the simple L.E. Wilson chamber types will allow you to nmeasure what's happening when you start adjusting the dies. What you're looking for here is to set the shoulder back to approximately the dimensions of a new, unfired loaded round. Once you have a measurement for cases that have been fired in your chamber, you can look towards setting the shoulder back to about .003"-.004" under fired dimensions, but for starters, just use an unfired round. Use the gage to adjust the sizing die to a point where the resized cases have the same datum line dimension as the unfired rounds, and see if these cases chamber properly. If not, then it has to be a radial dimension issue that will need to be cured. That may entail a Small Base die.
SB dies aren't always required for Service Rifles, but they don't hurt a thing and can solve a ton of problems. As far as the "excessive brass working" that many get so excited about, it's nothing, and well worth avoiding the potential problems I mentioned. Many handloaders aren't fully aware of this, but standard FL dies do NOT resize cases back to their original unfired dimensions. SB dies get a lot closer, and that's what we're looking for here. Using the SB dies, in conjunction with the case gage to set your datum lines should resolve the chambering issues completely. While the advice to adjust the bottom of the die down to the shell holder is what's specified in most manufacturers instruction, it really is a "one size fits all" approach. It works in most instances, but isn't really the ideal way to adjust these things. You may find that the die will work properly when adjusted that way. Or, it may be sizing the brass excessively. On the flip side, it may also not be pushing the shoulder back far enough, and need to have some material removed (ground) off either the shell holder or die to reach the proper fit; I've seen several instances of all three.
Start there, and see what happens. Give us an update, and if there's any issues that remain, we'll dig a bit deeper. Either way, we'll get it taken care of.
No problem at all, and I think the Precision Mic will help here. You might also look at teh bump gages that Sinclair and a couple others sell as well. Both of these gages will measure the same thing; the actual length from case head to datum line, which is where we determine our headspace dimension. All of the measurements you've listed here (with the exception of the OAL) appear to be diameter readings, and I don't think that's your problem. The Precision Mic or bump gages will allow you to verify that you are in fact pushing the shoulder back far enough to allow the cartridge to fully enter the chamber, and the bolt to close without binding anything. It also enures that the case is entering the die far enough to take the radial measurments down to where they should be. One other thing; make sure you run these slowly when you resize. Running the case all the way to the cam point (where the press toggles over), holditthere, at least to a count of five. Brass is naturally resiliant and has a spring back factor, which is precisely what makes it the material best suited to making cases. However, that same resilliancy allows it to spring back out a bit if it's simply run into a die for a moment and then pulled right back out. All the way to the top of the stroke, a count of five, and then lower the ram. It makes a difference.
I'm curious as to why the OAL is so short, though? Nominal specs for a 5.56 or 223 Rem is going to be right around 2.260". I generally run mine at 2.250" to 2.255" just to allow a little clearance with the front of the mag. What bullets are you using, and how did you arrive at the 2.220"-2.227" dimension?