So it may be linked to size after all! I have played around with the settings inside /etc/initramfs-tools/initramfs.conf. If I switch from the default MODULES=most to MODULES=dep, the system works and I am able to reboot correctly with /boot/initrd.img! I am going to check if I can load OverlayFS in this way next!
The resulting file is much smaller, even smaller than the default initrd:
-rw-r--r-- 1 root root 7160133 Aug 2 11:09 initrd
lrwxrwxrwx 1 root root 24 Jul 21 20:54 initrd.img -> initrd.img-4.9.253-tegra
-rw-r--r-- 1 root root 5959603 Oct 4 14:49 initrd.img-4.9.253-tegra