I know you said 'apart from the download options,' but this really is the easiest way to back your tree up:
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On the family you want to back up, click on 'Download/export this family'.
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Select 'FamilyScript'.
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Click 'Download'.
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Save the file which downloads (I recommend in 'My Documents' or equivalent'). Make sure you give it a name you can easily recognise.
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Go to the account you want to export the tree to.
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Go to 'My Account', and click on 'Create or import new family'.
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Click on 'Import GEDCOM or FamilyScript'.
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Click 'Browse' and find the tree's file where you saved it.
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Click 'Import', and then 'Finish Import'.
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Save the tree on the new account (use the normal 'Save' button).
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You should then be able to use the tree as normal.
If you just want a backup copy of the tree, only do steps 1-4. Steps 5-11 will put the tree onto another account, where it will be accessible as usual.
Note that you can also export using GEDCOM, but I think it might be a bit trickier.
I hope this helps!