Tuck nailed it with shooting into the wind and start with the HMR, the rimfires shot into the wind dont seam to scare the dogs much. The 204 will be a big asset, I would take enough to shoot at least 200 rounds a day through it, set it in the shade every 10 rounds or so with the chamber open to cool!
I personaly would get the Savage in 223 as the 22-250 is going to heat up a LOT faster=I've seen guy burn 22-250 barrels out in one day trying to keep up to 223s. The 223 ammo is usually a lot cheaper too!
I usually take at least 4 guns doggin.
The little CZ American shooting 40 Vamaxes always goes.
The old J action single shot 243 shooting 55Nosler always goes
Early season a rimfire goes....either the 77/22 or Savage HMR
One long range rig....Varies 243,6-284,7mag or 338 Edge
Either the 204 Savage shooting 32 grainers or the Savage 20PPC shooting 39 Sierras.Early season the 204 and the 20PPC late summer.
A good town can keep 5 guns hot.....With the sun out even the rimfire will warm up.