I'm trying to get an idea of what's the heaviest bullet I can load.

I have a 10FCP in 308win with a 20" fluted barrel, 1:10 twist.

Shooting factory stuff was.. eh, I dunno. On good days, I've shot .25-MOA groups at 100yds with Federal Gold Medal Match 175s, so I know it's definitely a very capable rifle.
I've learned that it doesn't like anything less than 168 though. Just kinda projectile-vomits them downrange, and precision on target is anybody's guess. The 147gr M80 milsurp stuff is good for blowing up watermelons, that's it. That stuff shoots a lot better through my M1A than my Savage. And the 150/155gr zone isn't much better. Things start to come together at 168, (seem to) flourish at 175, but I've never shot any factory ammo heavier than 175gr.

I just got into reloading a couple months ago and I started out with my first batch being Sierra 175gr MatchKing BTHP's. They worked great, and if that was the heaviest I should go then I'll be plenty satisfied with that. But I'm trying to get a better idea of how far I can (safely) go.

In my Lyman reloading manual, in the 308Win data section, the heaviest bullet listed is the Sierra 200gr MatchKing.
I've combed through the bullet offerings from some of the major bullet manufacturers and the heaviest 30cal bullet I can find is the Seirra 240gr MatchKing. My guess is that this is for rounds like .300WM or .300RUM, but I was wondering if anybody knew approximately where to draw the line for a 20" 1:10 barrel. I've found some rough-idea information, but there was never consideration for barrel length. The very few places where I did find information, either (a) had NO data on what barrel length was used for testing, or (b) used a barrel way longer than mine like 26" for example.

Any help is appreciated! Thanks yall :)