That would about reinforce the suggestions above that you will want to use FLS die - or perhaps Small Base dies if any are pump, lever or semi-auto. Is a thing that some will do called "partial full length" sizing - a way to get most of the "benefit" of neck sizing, with minimal disturbance of the fired case body - is easy enough to do with regular full length size dies - but I doubt that can be done for four rifles, all at same time.
It will be what you discover - is one thing to make ammo that goes "bang" - safely - and is usually "good enough" for most shooters, for most uses. Is typical that specialty guys will do more than that - tuning a particular piece of brass for a particular chamber - but is not really a beginner thing - first objective is to make lots, that work in your rifles - once comfortable doing that, then can get more fussy about various specialty techniques for a particular rifle and particular application. What a guy needs who wants to shoot a couple deer, versus a guy that wants to shoot 1000 yard gongs, versus a guy that want to shoot sub-.020" groups at 100 yards are all different. And many things that are valuable to one, are pretty much waste of time to another.
I have a few Model of 1917 Enfields - so from WWI - and the ammo from back then was called 1906 - so we no longer have that powder or those primers or those bullets - but a 30-06 from WWI was getting about 2700 fps with 150-ish grain bullets from those 26" barrels. Most modern people would consider that to be pretty dismal today - but was what those sights were calibrated for. So I had visions of doing similar - load up a box of many dozen rounds that could be used in any of the rifles - promptly ran into the thing of making them "good enough" for all, or specific to one. Turns out there are differences, one to the other - even the required bullet seating depth to get about .030 bullet jump to the lands is different - one rifle to the other - that might be a function of wear through use, manufacturing tolerances, or whatever.
Your tumbling thing might be un-related to your hand loading - in my limited experience with that - typically a function of bullet LENGTH (not weight) and the rate of twist in the barrel, and the muzzle velocity - a longer bullet needs to spin faster in air, versus a shorter bullet - to fly pointy end first. Muzzle velocity and twist rate of the rifling will influence the RPM on that bullet as it exits the muzzle - is possible with under-size for bore that the bullet skids or strips from the rifling as it goes down that bore, meaning it is not spinning fast enough as it leaves the barrel. That could mean that the bullet is undersize, or the bore is overly large diameter - if the rifling still looks as it should - typically from .0035" to .004" deep for many centerfire bores when new.