just as a note, removing/adding counters to chalice of the void in response to spell being played does not counters the spell.
Are you sure that's true? I think the abilities would go on the stack like so:
1st: spell (a Mox for the example's sake)
2nd: Chalice ability
3rd: Coretapper ability
Let's say the Chalice has zero counters and a player plays the Mox. Mox goes on the stack, and Chalice triggers because the CC of the Mox equals the number of counters (0). Then the Coretapper is activated. The 'Tapper resolves, giving the Chalice 1 counter, but the Mox is still countered because the Chalice already triggered.
It's sort of irrelevant though, because you could just tap the 'Tapper first.