There's no way of making non-internet connected iPods handle the rental expiry situation; as said above you would have to enforce a firmware upgrade on every single iPod ever made, which would be quite impossible.
Why would that be impossible? Apple could release a new firmware for iPods that supports a sync of Apple Music. iTunes would be updated as well so that it would know to check for the correct iPod firmware version before allowing the music to be copied over. And then the new iPod firmware would have a counter that would start as soon as it disconnects from iTunes. When/if the counter runs down, the firmware would no longer allow those songs to play. When you connect back to iTunes and you still have a valid Apple Music subscription and if so, it resets the iPod timer again.
If you didn't install the new firmware on your iPod, then iTunes would refuse to copy over music, as it does now.