To clarify, I think I would have to modify wubildr.mbr to search for a
different wubildr.
It is easy to create a wubildr.mbr which searches for a different wubildr. see Makefile of Wubi
/usr/lib/grub/i386-pc/grub-ntldr-img --grub2 --boot-file=wubildr -o build/winboot/wubildr.mbr
/usr/lib/grub/i386-pc/grub-ntldr-img is part of the package grub-pc-bin and it is really easy to change parameters. e.g.:
/usr/lib/grub/i386-pc/grub-ntldr-img --grub2 --boot-file=xxxxldr -o xxxxldr.mbr
This creates a xxxxldr.mbr which searches for xxxxldr .
But note: xxxxldr.mbr works in legacy BIOS mode (non-UEFI mode) only and you need a xxxxldr with different configuration files. If you just copy wubildr to xxxxldr it loads the same Wubi installation.
Wubi on Windows 10
If you intend to use Windows 10 in UEFI mode, better to use a customized GRUB2 loader for UEFI. see Makefile of a Wubi for UEFI
grub-mkimage -O x86_64-efi -c build/winboot/wubildr-bootstrap.cfg -m build/winboot/wubildr.tar -o build/winboot/EFI/grubx64.efi \
loadenv part_msdos part_gpt fat ntfs ext2 ntfscomp iso9660 loopback search linux linuxefi boot minicmd cat cpuid chain halt help ls reboot \
echo test configfile gzio normal sleep memdisk tar font gfxterm gettext true efi_gop efi_uga video_bochs video_cirrus probe efifwsetup \
all_video gfxterm_background png gfxmenu