How to schedule time-of-day upgrades

Not an answer to your exact issue but a workaround that presents you with significant benefits: why don't you just use a proxy?

There are numerous options but I'd start with squid-deb-proxy. You'll need one machine to serve as the host but this could easily be one of the machines you're dealing with. Similarly it could be a separate server. Doesn't need to be powerful.

The idea is updated packages need only be downloaded once. They get cached and all the other machines download from the local cache.

You still need to stagger the update process. One machine needs to download the updates to fill the cache. You could use one machine to download the updates at night (using a simple @daily cron job -- happens at midnight). The other machines could be turned off over night (saving a lot of money) and then could just grab their updates when they like. They'd only use internal bandwidth so would fly.

Some tips on setting it up can be read here.

Looks like you are using two independent update mechanisms: cron-apt and the Update Manager. Try disabling automatic updates in the Update Manager. If cron-apt is configured correctly, you will get a notification email each time a new update is installed.