In my opinion, we could do the trick only with partuuid support on grub-probe.
Partuuid changes, its bad idea set on stone. Much better work with fs labels.
1) get partition grub spec with grub-search
2) get partuuid with patched grub-probe
Defining this function,

function label2partuuid{
LABEL=$1
search --no-floppy --label --set=GRUBPART $LABEL
probe --fs-partuuid --set PTUUID $GRUBPART
}
Changing kernel line,
root=PARTUUID=$PTUUID

Great news for ramdiskless systems if done.
Does your patched probe allow this?

This is a request to update grub-probe and 10_linux to support the Linux kernel's root=PARTUUID=... parameter.

Currently, grub-mkconfig passes the Linux kernel's device name in the root parameter when booting a Linux system without an initramfs.  However, if the devices get reordered then the system will fail to boot.  Current workarounds for this is to either generate an initramfs that can mount the rootfs via UUID, or to manually generate or update grub.cfg.

This patch updates grub-probe so that it can return the PARTUUID of MBR and GPT volumes and enables 10_linux to pass the PARTUUID via the kernel's root option.  This allows systems to automatically use PARTUUID (root=PARTUUID=...) when an initramfs isn't present.

I have attached the a patch with the requested change and an example grub.cfg.