Just to see if I'm clear on the disagreement here: it's about whether or not it's valid to use "there is a unique solution" as part of the constraints?
Because I had started by assuming that since hint 5 is the only thing that constrains digit four, in order to have a unique solution, the first three digits must sum to either eight or zero. And that still seems obviously true to me.
But your position is that "there is a unique solution" is sort of an external check and may not be used as an actual constraint? I can see that if you're not allowed to say "there is a unique solution, therefore the digits must sum to 8," then you're left with "IF the OTHER hints fail to force the digits to sum to 8, THEN you don't have a unique solution." And that makes hints 1 and 4 are NOT redundant in the yes/yes/no case for hints 2/3/5.
Do I have that right?
It still does seem very strange to me that unique solution would not be an allowable constraint when non-redundant hints is. So yeah, seems like a "both reasonings are the other way around" problem, and therefore a poorly-designed puzzle. But hey, game jam.