The easiest way is to clone your Mac to an external hard drive with Carbon Copy Cloner or SuperDuper. Boot from the cloned exernal drive and use Disk utility to reformat the internal drive. Then clone to the Mac with the external drive as a source. Regardless of how you proceed you better have a backup if you value your data. Time Machine is not bootable so is of limited usefulness.
Try shrinking the partition. Then move it back to full size once you were able to apply and get the extra GBs (80 is a good number).
And never make such changes well you should have backups from day one regardless, just more so.
Cloning means that the restore will optimize / consolide and leave you with free space that is no longer fragmented as well.
Then just boot off the clone, do the restore and then you can run BCA again.