Saving a schematic with noteblocks saves instrument and note, so building it on stone and pasting it on wool still gives the stone sound.

I have looked but see no option to NOT save instrument state of the underlying block.

Does providing block update manually (place something near noteblock, or maybe right-click it) - fix it?

Activation with redstone, no
Right-clicking (change of note) going over max so it start back at 0 and increase again, no
Manually placing block near noteblock, no

Manually placing block under noteblock, yes

Work with /fill too, seems schematic has to be placed first.
Should have mentioned I am using creative

Well, the schematic obviously stores all data possible, and when you paste a schematic in single player, the mod currently purposefully prevents all block updates and such to prevent triggering any redstone circuitry. So as far as I'm concerned everything is working as intended.

I guess I could add an option to do the normal block updates when pasting though. Not sure if that alone would properly update the note blocks, but I guess it should.

Aren't noteblock's part of those block's that need special update, with direction (in this case from below)? I wasn't digging code myself, so i might misunderstood something, better if you ask someone who did...