First, I would strongly advise against this.
The Thaum is a very action-intensive class, so introducing a mandatory two-action activity with no upgrades to it will probably not feel very good.
Then there is the balance problem. The Thaum gets their weakness stuff only against one target, but their 2x damage die bonus to damage from Implement's Empowerment applies to every target they would hit with the weapon. Which gets extremely strong very quickly.
The closest equivalent to this is the repeating hand crossbow. d6, 60ft range and five shots, after which you need to spend a full turn reloading. And that's an advanced weapon. I personally think this thing is underpowered af, but I think you can see the problem.
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If you want to go through with it regardless, I would go with what you proposed. Except the range, I would make that 30ft. 20ft more often then not feels like you basically don't have range at all. And they will already have to many actions they need to do without moving all the time. Other than that, making it use d4s would be more balanced, but rolling d4s feels bad, so screw that ^^.
This whole thing is only really a problem when it overshadows the other people in that game, though. If that isn't an issue, then just do it.