That’s a very easily solved problem. You generate a code-signing certificate (already used all over the place, and why Windows occasionally tells you that software “isn’t trusted”).
You then verify that certificate in the presence of observers from all parties. At the same time that you verify the anti-tamper tags on the ballot boxes.
The parties only have to trust the person they assigned as an observer.
That’s a very easily solved problem. You generate a code-signing certificate (already used all over the place, and why Windows occasionally tells you that software “isn’t trusted”).
You then verify that certificate in the presence of observers from all parties. At the same time that you verify the anti-tamper tags on the ballot boxes.
The parties only have to trust the person they assigned as an observer.