Professor if you cannot get 220 grain bullets I would not hesitate to use 200 grain Nosler Partitions. I have used them with great results.
I never used the 220 gr Core Lock but I used a 30-30 and 303 with Core Locks (170 and 180 gr) when I was a boy. The Core Locks seemed to be a bit softer then Nosler Partitions. My personal opinion is that a 220 gr bullet makes sense for soft projectiles like the Core Lock. If you have something tougher like a Partition the extra weight is probably not necessary unless you are driving the bullet through a moose's shoulder bones.
This spring I shot a small black bear with a 308 loaded with 200 gr. Partition bullets. It was very close range so we can assume the 308 performed roughly like a 30-06 would at longer range. The 200 grain bullet penetrated through both sides of the bear's ribs but opened up enough to cause massive internal damage. I don't think a tougher or heavier bullet would have been more effective.
Later a young friend of mine shot a caribou with a 308 using my 200 gr. load at about 180 yards. The bullet penetrated through both sides of the caribou's rig cage and exited out the far side. The caribou died within a few seconds. Internal damage to the caribou was a bit less, probably because of lower velocity at long range. For a 30-06 at longer range I think a 220 gr Partition might be a bit too tough. Impact velocity will be relatively low and the bullet might not expand fully. I'd stick with a 200 gr or even a 180 grain bullet.
Just my thoughts but you've shot a lot more animals then I have so take it with a grain of salt. Below is the caribou taken with the 200 gr Partition to give you an idea of the size. You can see the exit wound on the right, not particularly large.
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This hunt was a special one by the way, that boy is an Alaskan Native friend of mine. This caribou was the end of a year long quest to get him his first kill.
For what its worth I also shot a similar sized caribou with a 180 gr SST out of the same 308. I could not see much difference between the two bullets. Both penetrated and blew a big hole in the lungs. If anything the softer SST might have been a bit better.