A 32-bit grub bootloader will boot a 64-bit Linux image compiled with the CONFIG_EFI_MIXED option using the "linux" and "initrd" commands.
Note that these Grub commands execute EFI's ExitBootServices() prior to starting the kernel. Thus the kernel cannot use secure boot nor can it access the ROMs of PCI slots (most notably the BIOS of the graphics' card).
An alternative is to run the "shim" bootloader and then Grub and use Grub's linuxefi and linuxrdefi commands. These don't run ExitBootServices() but call into a EFI stub in the kernel which copies out ROMs, etc and then calls ExitBootServices() itself before starting the kernel proper. Attempting to run Grub's "linuxefi" command without the shim bootloader results in a "incorrect checksum" error, regardless of the presence or otherwise of secure boot. Unfortunately this approach has two issues: (1) the kernel must be 32-bit and (2) there is currently a bug in the 32-bit EFI stub which prevents the kernel from starting (it hangs with no output).
The bug is notorious. Moreover some 64-bit linux images fail, strongly suggesting some alignment or data-overwriting issue.
The only way forward to get the result you want is to modify the kernel so that it can be started with a 32-bit EFI stub and then transition to the 64-bit kernel proper. It is possible that the author of CONFIG_EFI_MIXED is working on this, perhaps you could email them.