After much blood, sweat, and reading of bad writing on Metalink :), I solved the problem. Here is my solution for posterity:
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(I'm leaving out a *lot* of steps I went through to figure this out!):
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Edit init.ora and try each control file in turn until you find one that Oracle likes (it will spit more errors about your control file being out of sync if it doesn't like the one you chose).
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startup mount<br>
recover database using backup controlfile<br>
CANCEL
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Add these two lines to your init.ora file:<br>
_allow_resetlogs_corruption=true<br>
fast_start_parallel_rollback=false<br>
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shutdown<br>
startup
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Presto! Now I'm doing a full export, and will recreate the database and import the data.
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Even after getting a successful startup, which should have reconciled everything, it will not start up without fast_start_parallel_rollback set to false.
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At this point, only the control file you've been working with is valid; the others are hopelessly out of date. I'm not entirely sure what the recovery process is for that, but it doesn't matter since everything's getting blown away shortly.
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Time to read up on archive logs. I have a sneaking suspicion that doing nightly dumps is really not all that's required here! :)
