I am quite an amateur when it comes to woodworking, but I am very pragmatic and have done as much research as I can think to do so I don't mess anything up. But I can't really find anything to suggest if this idea holds any water (or any weight at all)
To attach the splines to the wall I want it to be as sleek as possible, and I came up with the idea to use IKEA's Ekby Bjärnum on their side on the top and bottom of each spline. (You can see the pictures below)
Now my question is if this will completely compromise the load that the Ekby Bjärnum can hold? IKEA claims that they can hold 15kg, but it wouldn't surprise me if this was a low estimate.