What's the problem you're finding with shed ply, is it too many patches, voids, quality of surface veneer ply, lack of flatness?
Lack of flatness is something even the most expensive ply often suffers from, if that's the main problem then you either have to select your own sheets in person or switch to MDF. If it's voids then you won't find a huge improvement unless you go to top of the range marine ply, if it's too many patches then look for best Baltic birch ply with one or both faces designated "S" for show, alternatively look at hardwood face veneered Baltic ply.
Unfortunately there's not much avoiding the fact that with ply quality doesn't come cheap.
Good luck.