When you get to the partition table by selecting "Something Else", instead of deleting the old partition(s) and adding new ones for Mint, just use the "Change" button at the bottom of the table to edit the existing partitions.
Click on a partition you want to replace and click "Change" a partition edit window will open. Leave all partition parameters the same, just click "Format the partition as..." and select your file system choice from the drop down menu. The partition will be formatted (overwriting the existing OS) and the selected Mint partition (root, /home, etc.) will be installed. But for /home dont use the format option.
For Grub installation, either click on the drop down menu at the bottom of the partitioning page and select the location for Grub installation, or just leave this alone and take the default installation. The default is /dev/sda. This will install Mint's Grub in the mbr over any existing bootloader (Ubuntu Grub, Windows, etc.), and set up the dual boot menu automatically.
Of course, you'll need to reinstall all the additional programs and settings you installed originally. You may be able to backup and copy all your settings/hidden files back into home to ensure you keep your settings but this may not work totally.