"I suspect it does" Is that just an assumtion? Or do you actually know?"
I can't see your Lyman die and Redding stem so I can't know anything but I suspect you don't have the die body and stem set up properly. If you want a longer OAL you sure won't get it by screwing the seating stem down but I'm not sure I understand what you can't get it to do! Try this:
1. First, run an empty but sized case fully up into your seater.
2. Turn the seater die body down until the case mouth lightly contacts the internal crimping ring; then turn the die body back UP about a quarter turn - no more - and tighten the lock the ring right there.
3. Back your Redding seater stem up, way up.
4. Place a bullet normally and run the case back up to seat the bullet; continue lowering and raising the case while slowly turning the seating stem down in small steps until you have the OAL you want.
That will get you the most adjustment lattitude possible, bet you'll be fine. But, if not, you've done all that can be done so use the original Lyman seater stem. And you likely won't need to drill the seating cup deeper but if you do it sure isn't difficult.