All this turned out to be user error: the instructions for the Hornady FL sizing die indicated that you should screw it in so that it touches the shell holder and then adjust as necessary by testing each round in the chamber of the rifle you're loading for and making 1/8 - 1/4 turns. Unfortunately, I put it in touching the shell holder and then never adjusted it. Once I actually got hands-on with FALex's rifle, 1/4 turn was enough to get the cartridges seating normally.
I had another question while I have the experts on-hand: I discovered while getting setup for loading FALex's rifle that my Lee caselength gauge was allowing the brass to be trimmed MUCH lower than spec (minimum of .020", sometimes as much as .050"!). I'm tempted, in the name of consistency, to trash a lot of this brass. Most has been shot at least 5 times and some appears to be hardening because my chamfer tools are beginning to make irregular cuts in it. Getting more brass isn't a huge deal, just wondering if I'm sweating the petty things.
Thanks again to everyone who shared their experience and advice!
Mike