You allready have 2 308's, so I would not want another UNLESS your Encore barrel does not group well. If it does then I would go with the 300WM hands down. You asked about experience with these rounds, I have shot the 308, 7RM & 300WM a bunch. For several years I was on a 7RM kick & I owned 3 7rm's at that time. I shot a bunch of game with them & the 7 works well, it will shoot a 160 for example at about the same speed & traj as the 180 in a 300WM, or a 140 will fly about the same as a 165 in a 300WM & so on, therefore the 2 are very close in trajectory. The difference between the 2 is energy/power. The 180 hits very hard, but you can load the 200 Accubond up to 2,900 or so with Retumbo or RL25 & it is in a diff. league than anything you can load in the 7RM. For rifles in this catagory I decided the 300 was better for me & over 20 years later I don't regret it at all. You mention Moose & Elk & for being able to shoot the animals at any reasonable angle with a heavy bullet & trajectory if you decide to shoot a little longer range later, (you probably will) gives you an additional advantage you don't currently enjoy.
The only advantage the 7 would have is less recoil than the 300, but a 1" Sims or Pac. pad would take care of that, the 300 is quite controllable IF you set up your rifle properly. Plus, in a pinch you would have the same cal. bullets.
Yea, the 300 for sure.