Turns out the missus had bought me a karcher "K3 HR Car & Deck" ages ago, as a birthday gift, but I never bothered to set it up at the old rental but out it came (from the box) for the new house
Took ages, but here's a direct example of the difference the "cleaning" made (mostly just focusing the high pressure water onto tiny spots haha)... got it done before the housewarming (~17th Aug 2024), but took this photo moments ago:
It took most of two days to get the cleaning properly done around the back sections of the house