You are correct that you can remove the Adagio OE historical files and restart, allowing you to bring back the Softline Invoice History data. Just make sure that the orders and invoices you have posted in Adagio still exist in the current file (ie haven't been purged yet) - you cannot get these back, short of restoring the entire Oe database.

The Historical files are prefixed with OEHH or OEHL (header and details) - there are quite a few of them. Be careful not to remove any of the OEHEAD* data files, as these are used for current transactions.

Day End Processing does not purge history; you must have run the Purge History function and not realized the dates.