My S8 has a similar problem with always blowing hot. I swapped the valve block and now it is fine on the left but still blows hot on the right
I think these valve blocks are just getting to the age where they are worn out so even used ones aren't necessarily an option any more.
The one you have is an early version with the round motor. Its simple enough to swap the connector over or make an adapter. Its theoretically possible to swap the motors over, but if the screws are seized you could strip them and end up ruining the block.
The first thing I would try is the two sensors in the air box under the dash since they are cheap and easy to get to. If they have failed the hvac unit will be controlling the valve block accordingly. They didn't help at all in mine, but they're much easier to do than the whole block so worth a shot. 4D0820539 - about £20 iirc.