What, if any trouble do you have with full length sized cases? I had an Arisaki that my father in law had rebarreled to 30-06. I tried necksizing with the full length dies, but found that the sizing operation would actually move the shoulder forward slightly and the bolt would not close on what appeared to be a perfectly neck sized case. I wonder if you are not having the same or similar trouble. Try some full length sized cases to see what results you get. Also with the Lee collet die, you should feel the csae stop agains the die, then a little more pressure and there will be a tad more movement of the case in the die. This is described in the instructions. I wonder if this is to reset the shoulder. If you have concerns about the headspace of hte rifle, midway sells go, no go gauges pretty cheap or you should be able to have a smith check it out for you. But I'd try full length sizing first.
I first began necksizing only in my 30-30 in the hopes of improving the accuracy. Never could find that it did one lick of good. I'm not convinced that chambers which are cut to nominal sizes for the spec, will benifit from this practice. I suspect that a chamber with a tight neck whihc requires fitting of the brass benefits from such work, but run of the mill rifles? Nah. It may be that neck sizing will improve the case life, but a case that has been fired 10 or so times at full pressure has seen it's use. It is not like the 243 Winnie is so rare and brass so costly that squeezing every last shot from it matters.
You can probably get as much improved accuracy from weigh sorting your cases and deburring the flash hole as you can get fom neck sizing. Playing around with different primers can improve things too. My 357 Max shows a decided preference for CCI primers.