My suggestion is that you abandon Time Machine and back up with either CarbonCopyCloner or SuperDuper, instead.
Either of the above will give you a fully-bootable "clone" of your internal drive, in POFF (plain old finder format). You'll have a backup that is instantly mountable and also bootable -- invaluable to have around in a "moment of extreme need".
Carbon Copy Cloner can ever replicate the "recovery partition", and it can also "archive" old files (similar to ).
CCC is in every way SUPERIOR to Time Machine. I would recommend that you consider it.