Regardless of the tool used, your full backup is going to take a fair amount of time.  Keep in mind, the backup only backs up the *DATA* not the file, so your backup file(s) will be smaller than the database itself.

As for restoring to multiple files, no, you can only restore back to the same state it was when it was backed up.  So in your case, you'll have to restore to two 10TB files.  Those files can be restored to a different location than they were on originally (example, file 1 is on drive F:\ and file 2 on drive G:\, you can restore them to completely different drive letters,) but you can't split them up during the restore.

Any other solutions are going to involve a fair bit of work and time.  Plus, regardless, they're not going to appreciably impact the time it will take to run a full backup and may negatively impact that time.