Did you go ahead with this work and what glass did you go with? having work done to create a playroom in a north facing garden too. going with a combination of tiled and glass roof, just need to decide on which kind of glass ? blue for better temperature control or neutral.

You really want to try and avoid having the led reflected in the glass of the sky light. It would be best to put the tape in an aluminium profile and have an opal diffuser so there is no visible LED dotting. I would then mount this on its side and add a L or U shape channel in the same colour as the ledge so it’s conceals the led and profile so you won’t see it in the reflection. Done a quick sketch

Just a quick observation. To make the lighting over the island more consistent I would move the rooflight so that it does not overlap the island at all. Cleaner design. Think about what will be below it if anything. It is difficult to place lighting over a dining table if there is a rooflight above. I would lay out my propective furniture positions first before deciding on the best position for the rooflight. They provide far more light than conventional windows and you don't want half your sofa to fade for instance because the rooflight is directly above it. I would move the rooflight over towards the side opposite the kitchen. Also consider turning it through 90deg as it would mirror the island.

I would have the sides of the aperture slightly enlarged to have a 20mm shelf under the glass. I would then have LED strip light and if you worry about seeing a reflection of the lights you need a diffuser (commonly sold along side these lights).