First, I think your "experienced colleagues" were fucking with you or something, I'd throw that neck-sizer in the garbage can where it belongs and go back to the FL sizer with the expander ball removed like you were already doing... Bump the shoulder every time, in fact, do everything every time, the same every time, no skipping steps, so trimming every time too. IMO if a case doesn't need to be trimmed, then the cutter won't touch it, and there won't be any brass shavings to worry about cleaning up, but the only way to be totally sure that a case didn't need to be touched a little in order to be more alike to it's "brothers" is to try trimming it... It's all about consistency: we want to try and put our cartridges into as close to the same exact pre-fired state every time as we can manage before they go into the gun, any time we omit a step or skip something we're fucking with our consistency which is no bueno.
After the FL size, yes, follow it with a mandrel. Not only will it help with making neck tension more consistent, but arguably more importantly, it'll push any imperfections in the necks to the outside, so that where your bullets ride and touch the inside of the necks it'll be a much more consistent smooth surface case to case.
Neck turning? IDK, I don't shoot F-class so I don't see a need to neck turn, but for something like F-class it probably can't hurt. Since the point of turning necks is to make each neck more similar/alike to the last/next case, it might be worth doing in your discipline. YMMV.
Lastly: you didn't mention annealing... wtf? If you want maximum consistency without annealing every firing, forget it, won't happen.
There's a zillion reasons some guys come up with when trying to say annealing is optional, but really there's nothing to debate, it's science. If you don't anneal every firing, then you aren't shooting the same brass every load cycle. Once a piece of brass is fired, it's physically different than before (we can easily see it and have to resize it), but it's changed on a molecular level too (that we can't see), and it keeps on changing on a molecular level every firing, period. So, just like we resize the cases when reloading, we also need to anneal if we want to truly return them to their pre-fired state.
Remember what SD's actually mean: the closer your rounds end up to all being exactly the same, the lower the SD number you'll see.