Edgebanding would seem to be a fine solution, I personally didn't know where to find something like that so I didn't really consider it. I have 3/4" plywood under 2cm granite so there is a tiny portion of the plywood that extends below my bullnose edge. What the granite company had suggested when they heard I was using 3/4" was to paint the edges of the plywood to match the cabinets. My boxes are birch so the plywood wasn't too far off to begin with and it didn't make sense to me to try to match the Adel MB doors, but I decided to paint the edges black. That way they're effectively 'lost in the shadows', you don't notice the plywood at all. It's like the gaps between IKEA doors, you don't generally see the cabinet faces behind them because they're 3/4" back and generally in the dark unless a light shines directly into the opening (or there's light coming from the inside, all the gaps I was concerned about in my base cabinets went away once the tops were covered in plywood). Neither of these light placements seem likely to shine on the underlayment face. So in addition to edgebanding I'd say you could consider white paint to blend in with the cabinet box or black to make it disappear.
I had gone with the 3/4" due to my own concerns about 5/8" being too thin and the bullnose edge crashing with the doors, but heard different things from different people. As it turns out my granite installer used mortar between the stone and underlayment, mainly for leveling purposes but they also could have made up for height differences that way. Of course the pieces were big/heavy enough that they were tricky to install even with my perfectly-leveled 3/4" plywood, if they had to place them, level them AND play with the amount of mortar to build it up and clear the doors it would have taken a whole day instead of 3 hours I think..
But I guess I was more concerned than the granite company was because I didn't clearly understand just what they were going to do at installation, if the stone simply sat on 5/8" plywood (which isn't even 5/8" anymore) then it definitely would have been a tight fit for the doors & drawers, but with the mortar I think they were basically prepared for anything.