You have to build out PD extensions before formal PP extensions especially where there is a chance PD extensions no longer become PD (due to the PD rules).
If you want the finish of the PD extension to match that of the PP extension, you need somewhere on the existing house with that particular finish as it will then be considered similar. I’ve already mentioned the process you’d need to go through.
However and why are the LPA so strict on the actual colour of the render? The term ‘similar’ is just that... similar. It doesn’t state the ‘same’.
Just out of interest, is your existing house rendered?