I was in the midst of trying to rediscover a link to this via a Reddit forum when I stumbled across your post. This image you've given us here is indeed what I was referring to.This is the best that I can do, I only have access to it in 720p. If someone can get a 1080p screen cap, it might be clearer. It's at 6 minutes and 30 seconds into the episode.
You can make out the Klingon border outposts though. Spock's path does seem to go the correct direction for the map seen later in the episode.
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The founder of that Reddit thread also surmised the way the route could be mapped onto a composite image of the nearby UFP spaces. Your distance travelled - and mine as well - will certainly vary as the images we're looking at don't account for Z-axis travel distance yet.