Frankenmauser, I never intended to even try a 220 on deer, but a buddy begged me to loan him a rifle to shoot pigs on a weekend hunt. All I had extra was the 220, so I loaded up some 63 grain, flat base, Sierra softpoints (#1395, I think). They worked great on the pigs, so I tried them out on deer and they worked pretty good. Seems like I loaded them to about 3300 fps or so. So yes, a Gameking will work just fine, but a Partition would definitely be the way to go if I was going to actively deer hunt with the 220. Just DO NOT use an explosive bullet on deer. That's a bad idea, and yes I know that from experience. I'm not talking just theory here...
As for the FMJ bullets in the 220, I don't have any experience at all with them. I'd just expect varying results, with one time being a tiny hole in and tiny hole out and one time maybe the bullet tumbling in the deer and a huge mess. Buy and use the Partition or the Barnes.