First +1 to what Colin has said ... and he is correct, I've been too polite! Soooooo ...
Have you checked out the moodledata/temp/backup/ directory for those .log's I mentioned? Have you checked apache logs - the error log? Those investigations won't necessarily tell you *exactly* what went wrong but they could provide clues. Without doing that, and some other leg work (like turning on debugging), you are asking persons in this forum to do a 'Vulcan mind meld'. This is close to asking 'the thingy is broke! Please help me fix the thingy' when we don't know (may never know) what the 'thingy' is!!!
"There's no need to upgrade the installation of 2.0" ... meaning you don't have a site that is 2.0 from which these backups come, you have just the backups (a few dozen - so 30+?). Well, the one (assuming you've tried only one) restore you've tried failed. So it suggest to me that there *is* a need for at least a 2.2.highest version of Moodle running on your server to see if those backups can be restored at all.
Since you have dedicated server and it's Ubuntu you could install another Moodle server on it running a virtual apache - ie, main site is http://mymoodle.net (that's the 2.7) the older site could be http://migrations.mymoodle.net AND it could begin as a 2.2.highest using git. That site would have it's own code directory, database, and data directory. You could restore your backups there .. good chance more of them will succeed.
Would install that instance (migrations) using git since that will allow you to easily upgrade the migration site (once you have all the 2.0 backups restored and working) from 2.2. to 2.7.x. A site migration of the migrations.mymoodle.net like that would upgrade all your courses at once.
Bottom line ... the way you are doing this now, evidently won't work ... and won't be fixed to work. Afraid you are going to have to take a few steps back to move forward.
'spirit of thinkering', Ken