Scottish Highlander- You made a good choice by sticking with the .308. For the stag at 200 yards and under its as good as anything else you could get.
If you still get the itch for another rifle someday, (you will) look at some of the smaller, flatter shooting calibers. Might come in handy If you ever get an opportunity for a longer range hunt. Although the .308 is a good long range round as well. Some to consider might be .270, 6.5 creedmoor, .25-06, .257 wby (if you can afford the ammo) just to name a few
"Most people can't hit a flock of circus tents at those ranges." - P.O. Ackley