the idea may sound simple but it will be a lot of work. At least a day for each NDS file to rewrite, check, test and fix remaining errors mutliplied by the amount of nations.
Now on topic:
I dont know to what level you understand how the [SECTIONS] work in the NDS files.
I'll put down in theory first what you need to get a multibarrelled cannon in to the 17th century so you can do it yourself for the other nations and dont have to figure it out by staring at the NDS file.
Just check what's missing or different.
Evidently the basic entries, being
Now the multibarrel should be in the list in editor
Next is to make it buildable from the ART Depot under
Now you can build it ingame once you have builded an art depot.
Now we want to lock it so its not available at start of the game, but only after researching an upgrade. You can use the one already there but, then you also need to delete any related entries that have been done for that upgrade for imperia .Use Search function to see which sections hold this upgrade.
So you need to delete the entry from:
[ENABLED] - so its not available at start anymore
and set up the upgrades so it becomes available after upgrade:
[UPGRADE] - the upgrade
[UPGRADEPLACE] - where the upgrade is placed ( academy)
[UPGRADEENABLE] - so the upgrade is available at start of game in the academy
Thats all you need to get the multibarrel to be researchable trough an upgrade from the 17th century.
Now after looking at your NDS, i still see an entry in
[UNACCESSCONTROL] - you should not have entries here as this one is related to the IMPERAU, so both the aka upgrade and the multibarrel should be gone from here. Actually this whole section will be useless if you move it all to the 17thc century, as this entry blocks stuff after moving to the next century.
and you miss the entry
Those are the 2 mistakes I noticed immediately for your multibarrelled cannon.
Let me know if you change those and verify again all the needed entries if you still have an error with your multibarrels.