I rented an M3 there via BMW On Demand last month. Booked online a couple of weeks beforehand and it was fairly seamless picking it up in the BMW Welt on the day. Well worth doing. The car was on winter tyres so they advised not going above 200km/h!

I did ask about the BMW Classic car hire but they weren’t aware of it. I expect it’s run from a different area to On Demand.