Karcher K4 for Concrete

I have been cleaning my concrete drive and paths with a Karcher K4 for a couple of years.  I know the flow rate is poor and would definitely find the job faster with a K5 or K7.  Some of the concrete cleans up really well but I am left with black spots on some areas.  I know I used a neat bleach (and a lot of it) many years ago on the areas that clean up well.  I also know the K4 is only around 1,800 PSI, so slightly underpowered for concrete.  My question is would the K7 (around 2,600 PSI) be able to clean the black marks off?  Just wondering whether I would get better cleaning with a K7?  I know other brands may be suggested but I have a few tools (patio cleaner etc) that are Karcher so would prefer to stick with the brand if possible.

Here is a pic of the black spots: https://flic.kr/p/2iK5JqY