Strategy.Split / SplitWithDiagnostics already run ProfileDocument once
when the auto strategy resolves the chain. splitByHeadingsImpl was
rerunning the same O(N) pass on entry, so every auto-mode call paid
2x scan cost; SplitParentChild paid 2x per parent.
Pass the profile down through runTier and let splitters compute their
own only when called outside the auto path (where profile == nil).
wizardchen
151e999db1