As you are limited by the size, this is why Xone bite is a good option. you could look at G one Ultrabite too which it pretty similar however made for gravel so wider. Either way, you need the most aggressive UCI Cyclocross tyre to get the grip and remain within 33mm max.
I used to ride rocky hill which a mixture of shingle cotswolds stones, mud, sand and according to Strava 16% on panaracer comet 38-622 and the wheel was slipping a lot, that was "OK" for 100 to 200 meters but I would not do that for 8miles.
I remembered the XC setup I had 20yrs ago, check for evolutions and swap the tyres for Conti XKing front (all season) and Conti XKing rear (deep wet muddy winter) or RaceKing rear most of the year, I got up these hills without issue now.
Point being your las 8 miles are MTB-XC territory and is going to be the hardest so you have to compromise; with MTB "knobblyness", you will be slower on road tarmac but you will have a chance on these 8 last miles.