I hear you. I overseeded some TTTF around the same time. Got great results. Just keep mowing to let the KBG get some sunlight. You should be fine.

Agreed, and it's not unlike last year when warmer temperatures held on late and then shifted cold. I went from full summer garden to cleaning it out in the course of a single day.

Your KBG is questionable; it didn't have much time in the warmth to pre-germinate, but perhaps it got enough. Certainly you'll get some, although the days are no longer warm enough to encourage sprout. Winter survivability of KBG sprouts isn't usually a problem, so I wouldn't worry about that too much.

I'd be inclined to lightly seed just before a major snowfall on bare ground to get a dormant seeding in, and un-germinated seed from this seeding will also sprout a bit in April.

"So after it being a brutally hot summer, apparently we are in for a very cold and heavy snow winter."

No, no, a thousand times NO. My back aches just thinking about shoveling for hours on too many days. NOAA overnight freeze warning here. Ugh.