How to hot backup/snapshot an ext4 partition (in the absence of LVM)?

You don't need LVM. LVM just uses the device mapper, too. You can do that yourself. That may be a bit tricky with the root fs, though, as you probably have to modify the boot scripts.

You just need to put a DM device on top of the root device, e.g.

sectors="$(blockdev --getsz /dev/sda3)"
dmsetup create rootfs --table "0 ${sectors} linear /dev/sda3 0"

Something like this has to be put into the initrd boot scripts. Instead of /dev/sda3 you would then mount /dev/mapper/rootfs to /. Then you can make snapshots of the root fs (but have to do all the steps by hand with dmsetup; no black magic though). You just can't merge them back but that should not be a problem.