Riding an occasional split on off road on 28mm tyres is possible as I've done it myself,but riding the same sort of terrain every or most rides is a completely different thing,it puts tyres and rims at risk IME unless ridden very carefully,as well as compromising comfort.
95% of my rides are either 50/50 or 70/30 off/on road respectively some of it similar to the type of terrain you mention or worse and in no way would I ride those routes on anything less than a 40mm(37mm actual)tyres
I'm only putting forward the 33mm Jack Brown as an option to the Hyper question. Riding on that sort of terrain with such a high tyre pressure on what is essentially a racing wheel with a road based tyre says to me the Jack Brown is everything that a hyper replacement/alternate would be just fine for.
That you wouldn't ride less than 37/40mm is down to you, that's your preference, I would never ride off road that wide with a tyre I'd be using so much on road (though I've ridden 40s/42s but only on road/very, very smooth trails on the odd occasion as they are paper thin), the widest off/on road 700C tyre I actually use is 35mm, I save them for really muddy/gnarly routes.
As it is I don't know your style of riding, your weight, the pressures you run nor the amount of comfort you want and indeed when on the road the amount of speed you want to sacrifice riding such wide tyres. Which undoubtedly you will if riding 37/40s at lower pressures for your off road excursions.
I'm also guessing you've never ridden the Jack Brown's so can't actually offer any input as to how they ride at different pressures/differing terrains or on differing rim/wheel types so your opinion is just based on the fact they're 33mm and your own personal preference, not really much to go on is it?