I don't
think there's any SAFE way to do this (but I'm still reading).
If the machine won't install Peppermint 6 64bit in EUFI mode, then to install GRUB on a drive with a GPT partition table requires an EF02 bios_boot partition to be present on the drive.
I'm unsure how to achieve this without destroying Windows or Windows EFI booting .. or if the bios_boot partition can go anywhere as long as it's flagged correctly.
I'm trying to figure it out.
Did you try installing the 64bit version in UEFI mode ?
(ie. NOT in legacy BIOS mode, but with secureboot disabled)
Are you able to boot a Peppermint 6 64bit LiveCD/LiveUSB in UEFI mode (with secure boot disable) ?
If so, have you tried running boot-repair:
https://help.ubuntu.com/community/Boot-Repairwhilst in UEFI mode (with secure boot disabled) ?