I'm surprised at the question, actually: even if you put the Farragut incident sometime during the (early months of the) war, it looks like we're still in the same ballpark.
Clearly your scheme puts things earlier than the usual Okudachron scheme does. At about 2/3 of the way through season 2, "Obsession" would fall in early '68 by that scheme.
At the very least, the incident is in the past as of DSC's "present day." And it's entirely plausible to surmise that Kirk actually sat out all or most of the war.
The war begins on about May 12, 2256; the series then picks up six months later, in November, and the remainder of "Chapter One" of the season spans maybe about 6 weeks, through about the end of the year. If the Farragut incident was in early 2257, as per the Okuda scheme, it would fall during the 9 months that Discovery was missing due to its Mirror Universe jaunt.