Does anyone use these cup and core on deer and moose? A long shot would be 200 yds.
I've used 200 grain cup and core bullets out of a Pattern 14 sporter, chambered for 303 British, which would give similar velocities as those from most 308 Win sporting rifles with 20-22 inch bbls.
They worked very well on Moose, Bears, Deer, and Elk.
Most people are concerned about velocities, and in some cases with good reason.
I'm not sure why you want to shoot those heavy bullets from your 308Win? Maybe because that's what you have and can't afford today's components prices or you're getting to your last days of hunting and just don't want to purchase more stuff?
Doesn't matter really.
Yes, those 200 grain cup and core bullets will do the job very well.
Cup and core bullets are old tech, but are still very efficient. As such, you need to load accordingly.
The 308Win obviously doesn't have the case capacity to load those bullets to velocity levels that some feel are critical.
IMHO, a heavy bullet at relatively sedate velocities can do a lot of damage and penetrate through both sides of animals under 200 yards, when the bullet is placed in the boiler room.
41 grains of Varget, if you have any, will give you 2500fps with those bullets. Be careful though that load may be a bit hot. It's safe in my Remington 700.
A 200 grain bullet starting at 2500fps will easily do the job, if you do your part and get that bullet into the vitals.
You don't mention the shape of your bullets. Round nose or Spire Point, etc.
You also don't mention the twist rate of the rifling in your barrel or length.
All of those are deciding factors.
Most hunting rifles chambered for 308Win have 1-12 twist rates and you may not be able to get enough velocity out of a 20-22in barrel to stabilize those bullets, if they aren't flat based or flat base/round nose.