There are special FTX seating stems for at least RCBS and Redding dies.
I have loaded the .44 265gr FTX in 444 and 445 with them.
I am sure Hornady offers them as well seeing as how they are their bullets.
Otherwise they are a pain in the neck as you have seen.
I recommend getting the FTX seating stem from your die maker.
They also work for the regular Hornady 265 designed for the 444.
I gave up on the FTX as they are more trouble than they are worth IMHO especially in a lever rifle.
Hornady's solution of cutting the brass back leaves me cold.
I have loaded them in full length brass for use in my break action guns.
I don't think they offer much if any advantage over normal bullets at the velocities we are talking about.
Even at 2250 fps. they might add another 25 yards of point blank range.
Since you were given the bullets have fun with them but maybe start wondering if they are not a solution in search of a problem.
If anyone wants a box of the .44 265 FTX to experiment with PM me.
I could be convinced to part with them as I don't plan on loading many more, if any.
Hornady claims they are designed for 1300-2300 fps which is a pretty wide range.
In the 444 forum there were tales of them just zipping thru elk and not expanding properly.
Many 444 folks have gone to the heavy WFN bullets instead.
Veral Smith's bullet designs are almost universally acclaimed in the field.