I do not know what grub-efi does in the background.
With BIOS, when you install grub to an MBR, it also customizes core.img to know which partition to search to find the rest of grub. Core.img is not shown and is just in the sectors right after the MBR. That space does not exist in gpt partitions and with MBR you have to create bios_grub to have a place for core.img.
In your ubuntu efi partition, are there other files? Bootinfo script is only looking for the .efi files. Not sure then if the grub efi file includes the core.img code to know which UUID to search?
You could always backup both efi partition and experiment with just copying the efi/ubuntu folders into your Windows efi. It may be missing key parts like the core.img we have in BIOS or it may just be all you need?