One thing I have done a couple times in the past to reduce the amount of working the neck down from fired cases in factory chambers that were cut overly large is to neck down a larger caliber case that was a close match to my cartridge.
Three examples that I remember: I currently use 338 Win Mag brass to form 7mm Rem Mag cases. I anneal the necks after sizing down, outside neck turn, and have reduced the slop between the finished necks and the large chambers by about 0.0015". I've used 340 Weatherby brass to make 300 Win Mag brass but only reduced neck clearance by about 0.0005". And I make 280 AI brass from Lapua 30-06 brass, but this is in order to take advantage of the higher quality Lapua cases.
But in my experience, you'll only gain ~ 0.001" reduction in neck clearance by necking down a larger caliber case to a smaller caliber neck diameter. And I don't know if there are any 33, 35, 375, or 40 caliber cases that could be converted to 308 Win by stepping the necks down because that's a round I've never owned or reloaded for.
0.009" is on the high side for neck clearance for sure, even in a factory chamber.
Oh - sometimes just changing brands of brass will help reduce neck clearance by 0.001". Best way to figure that one out is to just take your dial calipers into the gun shop and ask if you can measure the neck diameters on some different brands of factory cartridges. The loaded bullets will all be the same diameter, so the brand of cases with the largest outside diameter will be the brand of brass you'd like to purchase.
One last tidbit. You haven't said how the rifle shoots. Zero runout is the goal, but if it drives tacks with 0.002" runout, then I'd be happy driving tacks no matter the runout.