200 rounds per day I think gets rid of all the hot shots, like .220 swift, 22-250, 22 br and 22 creed. 222 rem is a tack driver, but doesn't have the steam for 700 yards, and I think any of the .204 and .17 variants will be the same.
.223 ai with a fast twist and 70-90g bullets would foot the bill, and there are plenty of .223 actions available, as would the 6 ARC or a 6 fat rat. I don't know a lot of bolt guns that have a grendel bolt face, but it's easily done in an ar. 700 yards in Montana plains may be interesting, but they will do it. There are guys that will bush a bolt face, but I only know of people who have had it done.
Then is the 6br (br, brx, bra) based cases, those will play 700+ all day. 200 rounds is a lot to ask from any rifle, but with a good barrel I don't think there is an issue if you take breaks. Components are hard for anything, but lots of guys shooting them and plenty of data available. Low recoil, lots of bullet choices and good brass. 2850-2900 FPS on 108-110 g bullets I believe is the top end on these. I think this is the sweet spot for what you have listed.
You can use bigger cases to go faster, but 200 rounds on a .243 or 6 creed is a tall order. A 6.5 bullet wants more powder and I can't poo poo a .260 or a 6.5 creed, but for vermin I don't see any reason to try and hot rod them. If you don't hot rod them, the 6br cases win inside 700 yards.