Retumbo is a little slow for 180s. I made my best velocity with IMR 4831 and 190gr SMKs but they didn't shoot that well for me. I would try 4831 with the 180s should make 3100+ fps.
I have a great load in mine with 208gr A-MAXs but you can use the same load with your 200gr Gameking. I use 74 grains of IMR 7828ssc with the 208 and that's the book's max load for a 200, but I have no pressure signs and my primers aren't even flat. Start at 72gr and work up until you see pressure. I am getting 2950fps with that load and the accuracy is amazing! First and only group with this load printed a .176 thousandths three shot group at 100yds! Going to shoot is some more and see how it does.
When I was tinkering with the 190 Matchkings I couldn't get anything better than half inch groups and most were around 3/4 inch. My rifle just doesn't like them. I did achieve good speed but even the lighter loads didn't shoot. I tried 7828 with the 190s and my max load with it went 3050fps while the max load with IMR 4831 made 3125fps. I think Retumbo will be way too slow with anything lighter than a 208gr.
I recently helped a friend with his 300 Win and 215 bergers. He had retumbo which didn't work. ES values were high and accuracy was unacceptable. Switched to H-1000. ES values were low and it shot very accurately.
Can't imagine you will do better with a lighter bullet. Worth a try I suppose. You have the powder in hand. Let us know what happens.
I run 84 grains of it with a 180 SST or a 200 ELD-X.
Either way about it, it's a completely full case... and as others have said, it's almost too slow for that bullet weight.
RL22 or 25/H or I4831 would be a better choice....