I dont understand one thing: the centaur PC should be large because of its ''horse half'', right? Its not the human torso that would make it large, if I understang correctly. So, I think a good compromise would be to let the centaur occupy a ''Large'' space, but since the part that actually wields the weapons or grapple (I dont thing people would try to grapple or wield weapons with hooves), just specify in a specific trait that the centaur wield weapons and grapples as a medium creature. Problem solved.
So the Centaur would have larger blast/aura at the cost of having to squeeze in smaller places and being harder for him to take cover.
I'd let the extra equipment cost be a Dm fiat thing, like the druid's metal taboo.
For the minotaur, I'd give them a natural weapon that could deal the same as weapon+shield (since it doest require hands), so 1d8 should be plenty. Not as good as d10/d12 weapons, but lets you grapple while wielding horn and shield. I dont feel the necessity of having them large, but I'd give them the Long-Limbed trait from the Bugbear, to simulate the greater reach of a large creature, without having them actually large. They would carry as a large creature, attack on their turn as a large creature, without them being actually large.