What happens if we mass claim:
Assume 1 high priest, 1 aztec artifact bearer, 1 Cortes, 3 tribesmen (no tax collector)
Cortes claims to be a tribesman of course, so we see 4 "tribesmen".
Even though we have 1 lynch plus 3 nightkills, we can't just kill off all 4 "tribesmen" because Cortes is NK immune and will kill the priest who finds him.
Plan 3-kill: Claim, then choose the three most suspicious "tribesmen". Lynch one, assign one to the artifact bearer, and one to the high priest.
25% chance: Scum lynched, we win.
50% chance: Attempted sacrifice on Cortes, now we know who he is and have at least two town left to lynch him (since he will have NK'd someone, probably the priest not targeting him). We win.
25% chance: We lose.
So, 75% straight chance of success, assuming we pick at absolute random.
Plan 2-kill: Claim, lynch one, then have the High Priest kill someone (since they have to)
25% chance: Scum lynched, we win.
25% chance: High Priest hits Cortes and dies, lynch and we win.
50% chance: Scum NKs, probably High Priest. Left with 1 scum and 3 town, one of whom is artifact bearer.
Safer. Only 50% straight chance of instant win, but no 25% chance of losing.
Plan no-lynch: Claim, no lynch, assign someone to Priest and to Artifact Bearer.
50% chance: One of our NKers hits the Cortes, the other gets NK'd, left with Cortes + 2 tribesmen, we win.
50% chance: 1 scum and 3 town, same as previous plan except the scum chooses which of our power roles get to live.
Summary: Do we go for the 75% chance of an instant win, with the risk that we find the Cortes *least* scummy of four people? I will be one of those four people, by the way. Or do we play it safe with Plan 2-kill? Plan 2-kill seems marginally better than plan no-lynch.
After all this, I'm satisfied that a mass-claim is a decent, perhaps good, idea.