I would appreciate some info on what happens or how it happens when you move from 1:10 to 1:8 in this situation. For my level and application, it would be nice to know if it's something I would benefit enough from worrying about it.
Hopefully this isn't too basic for you. Don't mean to insult your intelligence.
The short story is that you need a certain rpm to stabilize a bullet. It depends on the shape of the bullet. Short fat things like handguns require much lower RPM (50,000 rpm) vs long skinny things like a rifle bullet (200,000 rpm).
Unlike the car analogy, properly balanced tires generally don't have to spin at 200,000 rpm, nor are their aerodynamic properties changed with normal automobile tire RPMs.
With bullets, faster twist isn't always gonna be better. 2 undeniable reasons, 1 somewhat controversial reason, and a 4th that probably isn't that significant unless you go to extremes.
1) Spinning an out of balance bullet (slight variations in jacket thickness, heterogeneous lead core, etc) really fast can cause it to fly funny.
2) Thin jacket or soft lead bullets can literally come apart due to the centrifugal forces if spun really fast. Shooting 110 VMAX in my 300 win mag causes this.
3) "Over-stabilization". A bullet actually needs a little instability in flight, and doesn't point directly into the wind. I believe it generally is designed to point up a little (weight towards the back). If you spin it crazy fast, it will stay that way, even when the bullet starts to drop, instead of tilting and pointing generally in the direction it's traveling. At fairly long range, when the bullet is angling steeply back towards the ground, it won't tilt down enough, and basically is belly flopping towards the ground instead of tipping as it flies. This would obviously increase the drag, potentially in an unpredictable way.
4) Twisting the bullet requires energy and friction. If you take it to the extreme, a 1:2 twist barrel has considerably longer lands/grooves than a 1:20 twist (think straight line distance vs a curvy road). That generates pressure, reduces velocity, etc.
Where the rubber meets the road for you?
With well constructed, modern projectiles, in weights relevant to your rifle, 1 and 2 are probably not much of a concern. Neither is 4 when you're talking 1:8 vs 1:10. 3 comes down to preference, and how far you intend to shoot, as my understanding suggests "over stabilization" becomes a problem as the trajectory steepens at long distance.
You'd probably be fine with either a 1:8 or 1:10 or anything in-between. The longer the bullet the more RPM it needs. For 300 WM, only the REALLY long bullets (>215 lead core, >200 solid copper) would potentially be understabilized in 1:10, and unless you wanna shoot really light bullets (160 or less), 1:8 should be fine.
The only caveat to the above is that you absolutely can
try for "perfect" stabilization, but only if you're certain you only wanna shoot a narrow range of projectiles. With long bullets, 1:8 might be a tiny bit better than 1:10, and vice versa for short bullets.