I'm one of the posters Boyd mentioned -- hopefully one of the creditable ones.
What those of us who advocate a false shoulder are saying is that if the case doesn't move forward in the chamber, two good things happen. The first is you stop the kind of case separations like you experienced. The second is the dimensions of the entire set of cases are more consistent, and given close-fitting dies, will give a longer life. Some of us even claim a slight improvement in accuracy, at the benchrest level, which can be slight indeed.
Your specific problem is the first, and you may not care about the second, which in any case has only anecdotal proof.
Jamming the bullet is suppose to keep the case from moving forward in he chamber. Try this test: load one more case as you did the first batch. Fire it. How does the primer look? Usually, they look flattened beyond what you would expect from the pressure you're running in a FF load. When headspace is large, I've seen some that reminded me of a solder splatter, like when you tin the iron & shake off excess.
If the primers look that way, you have your evidence the case is moving forward in the chamber. You could risk one more case by increasing the bullet tension to whatever you can muster. My guess is you will still see evidence of case movement on the primer.
But if not, you are almost there. Section the case to make sure there is no thinning just above the web. I suppose I'd do about five more -- including sectioning, since case wall thinning was the original problem -- to make sure the first one wasn't a "false positive." If everything's OK, you're home free.
By all means include lubing the case, unless you're interested in comparing lubed versus unlubed cases in fireforming. If you use water-soluble case lube, cleanup is easy, but cleanup isn't too bad if you use something like Kroil or WD-40.
It is possible that with a lubed case, even though it does move forward in the chamber, the stretching is more even, and you will get fewer separations. That may be enough for you. But the false shoulder isn't that much more work, and should solve the problem completely.
Edit:
As a sometimes fan of big 6mms, and one who has wildcatted a few, such as a 6/284 with the reamer held in .200, I can add that barrel life is not great on these. Sometimes as little as 800 rounds for benchrest performance, maybe as little as 2000 for highpower.
This, amongst other reasons, leads me to not fireform with a bullet. Close to ten percent of your barrel life just to form cases offends the cheapskate in me. If you don't use a bullet, the false shoulder makes the whole procedure much simpler. Fireforming with a wax plug and pistol powder puts far less heat in the barrel. Can't say how many rounds it takes off barrel life, but surely not as much as 40+ grains of a slow-burning powder.
Alternatively, if you do your own work or can get a chambering job done cheaply, get a dedicated fireforming barrel. Let it's throat burn out.