I would replace the barrel instead of bothering with the push-through die gizmo. The stock barrel will weaken the brass, causing separations near the feed ramp because of it's large tolerance in the breach.
The aftermarket barrels will not have these issues - so no "push through" brass gizmo necessary, and your brass stays nice and solid through several reloads.
The aftermarket barrels also have traditional rifling, so less build up of lead for using lead bullets.
BTW, I own a Lee 3-pcs. dieset, which works just fine once you set it up. I just use a sharpie marker on the threads and body of the dies to ensure consistent sizing/taper crimp. I occasionally check COAL and inspect the cartridges to ensure everything is right.
Like everyone else is saying, don't bother with the case trimmer, these brass aren't going to need trimming.