Hi Minimax, :welcome:
I have dabbled with slate art before, but years and years ago when there were probably less sealer products about. The lines do disappear outside, I really don't think any sealer will stop that, as any that last ouside will have an oil or resin action of sorts.
What you do is beautiful there, I can see the potential and am wondering if you are not making life needlessly difficult by not looking at colouring. Some of the guys here are experienced with grout pens, may that would work? just a thought, a felt tip point kind of action is really what you need, isn't it..