C# (Visual C# Interactive Compiler), 301 bytes
n=>Enumerable.Repeat(Enumerable.Range(1,n.Max(x=>x.Max())),n[0].Count).Aggregate((IEnumerable<IEnumerable<int>>)new[]{new int[0]},(a,b)=>a.SelectMany(x=>b.Select(y=>x.Append(y)))).Single(x=>n.All(l=>{int z=0;var i=x.ToList();var p=l.All(o=>o==i[z++]|o<1);x=x.Skip(1).Select((a,b)=>a+i[b]);return p;}))
Gymhgy
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