Sounds like the perfect excuse to employ the N+1 rule and get yourself a cyclocross bike......
BINGO! ! ! ! 
Having had a nice older Italian road bike with 23's on it there's no way I'd want to suffer through 38 miles of gravel with the poor thing. I was thinking the exact same thing as I read your post but Blues Dawg and tsl beat me to it.
Either a cylcocross or a nicer 29'er and put some 34 to 38 mm cyclocross tires on it. For that matter there's some pretty nice mountain bike tires with overlapping center knobs that roll pretty sweet on pavement at the higher end of the pressure range and would still work aces on that gravel. The rest of the time with platform pedals it would be a great casual quick errand bike or you may even feel the need to go and explore some trails ! ! ! !
.. oh sorry for suggesting such a madcap option....
