That same TOS episode had cloaking devices an amazing new concept, as well ship-to-ship visual communication not existing yet and the prevailing weaponry of the day being atomic bombs. Enterprise (as well as The Beginning script) and Discovery well and truly ignored that, introducing cloaking devices a century before. I don't think they'd have fretted any more about the 2259 date.
The novels did try to explain some of that away. Such as the Romulans refused to show themselves to their enemy or even communicate at all. And they did use atomic weapons in some instances (which they even did in "Balance of Terror"). I give Michael Martin credit for trying to tie the loose ends together and create a story that might explain some of the inconsistencies.
I do sort of think the timing of the war being in the late 2150s is sort of set. We know in canon sources the Federation was born in 2261, and was formed soon after the war. And Enterprise ended in 2154 or 55 (I forget which exactly) and war had not yet broken out. So canon sources seem pretty firm as to when the war could have taken place.
I doubt the current showrunners would do anything to contradict that, if for no other reason they don't seem very interested in exploring the 22nd century outside a few Easter egg references here and there.