If speed if your issue, then you don't want to restore directly from tape as disk is faster. However, the array that you have space on, is that shared with the storage groups? If so, you lose your array, and you've lost your online backup in addition to your in-use mailstores.
How many storage groups do you have? How many mail stores? Maybe you could implement more groups and stores, across different sets of disks. Then any individual backup and restore would be quicker, due to less data being involved.
Potentially, you could have a 'High Priority' set of mailboxes, and have those on their own store. That way, in the event of disaster, could you restore those first?