I went LiTime Lithium on my AT Overland camper build. Love it. Internal heating so it can charge no matter what the ambient temp is and bluetooth so I can monitor it from my phone. You won't need the Shunt if you go with this battery.
Caliber doesn't really matter. The particular bullet does. Each bullet is designed to expand down to a certain speed. Call or email the manufacturer of your bullet and find out. Could be 2500 FPS. Could be 1800 FPS. Wherever your gun and load puts the bullet at that minimum speed is your max...
You are on the right track. Any 700 that isn't broken that is properly bedded and floated and properly assembled and torqued should shoot as well as you can.
I have an old Sportsman 78 that has a beautiful BDL Gloss Monte Carlo Stock and a Zeiss Conquest on it. Shoots 130gr TSX groups touching...