Might try cam over. I use Redding dies but camming over will work with any die set and press. Just set the die so the ram touches the shell plate and give the FL die another 1/8 to maybe 3/16 turn in - that should work for about any tight chamber.
This is what I had to do, initially I wasn't bumping the shoulder enough and the cases were sticking when you would try to eject a live round. They ran fine otherwise.
I bought a small base die before I made the sizing die change and the small base didn't help, I ended up returning them. You may have a need for them if you use military brass as the stuff that comes out of a 240 might have the base of the case blown out more. Full length dies have been fine once I had it set up properly and I do resize military range pickup's.
For what it's worth the Hornady book and video said to set the sizer up when it touches the shell plate when in reality it needed another 1/4-1/2 turn past that point.