Hi Jack
I would go for a 223 - has all the attributes - including low recoil which is preferable for NV shooting - From my own experience of mounting my NV scope on my 234 and 6.5 CM - i sometimes missed the impact, especially when shooting off the bonnet of my 4x4. As said no cal is truly flat 250-300 yards , and if you do get one , you will probably by on your local rifle smiths Christmas card list but i know what you mean - flat as possible and good in wind too.
The lateral drift is really important , as you could get lulled into the trap of just shooting lighter and lighter bullets - going for max velocity, but these bullets tend to have low BC and can get blown about in the breeze at ranges over 250 yrds.
A few to consider
The 223,- shooting a 53 g Vmax (or similar) at around 3400fps - Zeroed 3/4 inch high at 100 - will a drop 2.1 inch at 250 yrds . the bullet will hit with approx 760 FPE . ( more than a 22 hornet at the muzzle)
22.250 does a splendid job at 300 yrds - sending the same bullet 300/ 400 fps faster - dropping 1.6 inches at 250yrds and and moving less in the wind too. It also hits with over 950 FPE. only real difference in cost is the few pence more in powder. As a foxing rifle barrel life isnt an issue. In years gone by , I was shooting over 300 fox per year, for many years. My favorite foxing cal is the 22.250 - so i am biased
The 20 cal are also perfect for that range - albeit the choice of rifles and bullets is less - the 39 grn SKB and 204 makes a excellent 300 yrd combo for NV.
Personally , give your criteria, i would go for the 223 - everything about the 223 is easy - fantastic selection of accurate rifles - different barrels twist and configurations - Ammo and all reloading stuff is easy to find and there is a huge selection of both cheap stuff and very high quality reloading components.
ATB
Alan