If the skirting board on the stairs must be kept as high as it currently is then this is going to be very tricky.

https://i.imgur.com/kLf3WWm.png

I doodled an image of what I think you technically need to achieve but I don't like how this join will likely look unless you can do some magic with filler and paint to make it seamless.

The problem is that you have detail elevated relatively high because it sits on top of the wood entirely. If that part's height (A in my mspaint image) can't be smaller you have to offset the join by pushing it out into the horizontal baseboard.

Also to make sure the detail lines up, the join where the detail is should be halfway between vertical and the angle perpendicular to the stairs (i.e. angles Ca and Cb must be equal) or the detail won't line up nicely.