You could always install in BIOS mode (to a GPT disk) and then convert it to boot in EFI mode by installing an EFI boot loader. It's not intended as a direct tutorial on how to do this, but my
EFI Boot Loaders for Linux page provides the information you'd need to do this. Pay particular attention to the boot loader installation page.
If you've already got Arch running in EFI mode, then you could do a side-by-side installation (doing the Mint install in EFI mode) and just add Mint to whatever EFI boot loader/boot manager you're already using. Once Mint is working to your satisfaction, you could then remove Arch from the picture, providing the boot loader doesn't depend on the Arch installation. (To the best of my knowledge, only GRUB 2 is likely to have such dependencies, and then only if it's configured in a way that I consider unwise. Sadly, Ubuntu (and probably Mint) sets up GRUB 2 in this unwise way.)