Please note this late breaking insight into your situation. Thanks to Dave A for this contribution.

I was reading the answer to the question on Recover through gap in archivelog file set?. The answer given was normally correct, but was incorrect in this case. I was able to witness this company recover the database (the dba there is friends with a dba in my company; small world)

The key here is that the reason the missing archive was requested by Oracle is that the tablespaces had been left in backup mode for a week. This means the SCN was frozen for a week. This means that the SCN in every backup would be the same for that week. Oracle would logically assume that it needed all archives to catch up from the start of that SCN, in reality, it doesn't.

Think about it this way, the database was backed up the previous night and was restored from that backup. Oracle wanted all archives from 6 or 7 days earlier to present because of the frozen SCN. In reality, it only needs the data from those archives written after the backup used for the restore.

The trick to get Oracle to recover given the missing archive log was to edit the previous archive log in sequence (after it was used) to make it look internally like the missing archive log. This wasn't easy as it isn't documented anywhere (that I know of) what needs to be done. A good hex editor comes in handy. At any rate it was successfully done and the database is fully recovered.