Using the Dillon in single stage mode won't absolve the flexing issue with the shellplate. It's just not as solid as a single shellholder concentrically on top of a press ram. If you have a true single stage press, try working there. If not, I'd recommend gettig one. It will be money well spent.
As for the die adjustment, you're making conflicting statements. Either it's almost touching, as you said in the first post, or it's all the way down as you said in your second post. It cannot be both. I'd venture to guess you need to size the brass down more, and really need to set up a single stage press to cam-over during sizing. Your description of the case body being too large in diameter is a dead indicator for not sizing down far enough, and it sounds like your Dillon press is not well suited to sizing brass for tjis particular situation.