I was wondering if you could further tune a load by sizing further up or down the case neck. Any thoughts?

Yes, i know sizing less of the neck is a help to accuracy,my targets prove this. With factory chambers, this lets the unsized part of the neck expand to the chamber, centering the round/bullet to the bore. Bushing dies and no expanded with neck turning work best, but is not needed. As for bullet neck tension, my guess is the brass will spring back only so much, or expand so much. In other words, it does not matter if the bullet expands the case neck or the expander, same effect. Trying different size bushings seems not to make a difference in a 1/2" moa rifle?

as a rule the closer the brass fits the chamber the better the accuracy. fire formed brass has more capacity.
by partial neck sizing you are changing bullet tension.
most neck sizing dies and bushing die move the brass back to the shoulder, a collet die squeezes the brass down onto a mandrel. with the neck dies and the bushing dies you will end up with a donut inside the case at the shoulder neck junction, which can lead to pressure problems. this donut is more pronounced with neck turning.
after a few firings of the cases you will start to feel diffrences in seating the bullets, some will go in easy others will feel hard or rough. as the neck tension changes so does the pressure and accuracy.
Dave

I THINK in the context that you're asking, No. Neck sizing the case only half way down the neck or all the way to the shoulder will not change the harmonics of the load to a measureable degree. Or if you are asking if a harder or lighter bullet pull will change the harmonics, again, I don't think that will change the load.
There are certain things that you can do to your cases to make a load shot to its potential but if the harmonics are not there, that is to say a balance between powder, rifle, bullet, primer, your case prep can take you only so far.

if the base of your bullet is still in the case neck there are some definate advantages to partial n/sizing.
if you are looking to change neck tension just firing the brass is doing that somewhat for you.
but you can just buy expander balls of different sizes to find out also.
i.e.
i use 5 thou neck tension on one load in my 308 with a very full[like 105% density] case of powder and the neck tension was the final pay off.
but some other rifles like a slip fit almost no neck tension.
and most fall in between somewhere around 2-3 thou is built into most die sets.

Pretty much everything you do differently in putting cartridges together will change the load's "accuracy" somewhat.

Usually, though, a single small change will not be enough to alter accuracy to the point you can "fer sure" know it. That's especially true with hunting rifles as opposed to target rifles.

Still, sometimes things we never expect to have an influence do alter accuracy big-time. To find out, you have to try them in your ammo and your rifle, AND keep careful records. And you have to try them numerous times, on different days...other wise the weather, your mental "set" that day, and lots of other things may be the cause of an apparent change (or no apparent change) and you won't know it without several different days' data to look at.

Just remember, changes for the worse seem to be easier to come by than changes for the better. So believe the data, don't make excuses for worse groups. (We all do, but I am reminding myself with that remark as much as anyone else...)