You really want the thin veneer, that’s between 0.6 and 0.8mm thick. 3.5mm is far too thick without sanding most of it away to that sort of thickness or you will have trouble with tuner post height. Adding a 0.8mm fibreboard veneer with paint and clear coat on top on my two SG and my ES-1 builds only left the bare minimum of post below the hole showing with the vintage Kluson tuners I fitted on them, barely enough to get 2 wraps on my bottom E strings.

If you can’t find anything thinner that’s suitable, then I’d stick the ebony on and after clamping and leaving overnight, trim it back to the headstock shape and then sand it down until it is the right thickness. I think it will be much easier to sand in place than on its own as a sheet.