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Again, I'm so sorry to hear it.
But I can't believe that they could not provide you with the database backup. If they got you all the other files, then obviously they still have access to the server, right?
I would ask them to explain to you what these files are, and how do you suppose to use them? Maybe they could convert these files to a mysql format?
Another way to get back your content, even if it would be very time consuming, is to use www.archive.org and then copy individual pages from Publisher there, e.g. your recipes.
Maybe you could even create a script that would go through all the Publisher posts by "id" number, and extract them from www.archive.org? Just thinking here loud...
Check your PM...