There's a number of aspects of what you said that are inaccurate, and I believe the approach you're taking is deficient in a number of areas.
Let me cover a few of these off:
1. Cloud access does not lead to wasting time with flash games.
Firstly, I think you are confusing cloud computing with Internet access. Leverage a cloud service (e.g. Google Apps or some SaaS based learning service) is completely different to unfettered internet access to play flash games. If your school chose to use Google Apps or Office 365 it doesn't all of a sudden mean a deluge of flash games.
2. Chromebooks can be managed with Chrome Management Console
With the Chrome Management Console you can control a vast array of policies - such as URLs that can be visited, what can be installed etc. All reasonably similar to the level of control you may have now on your windows machines. However, Chromebooks go beyond this as it is much harder for a student to bypass the controls that Chromebooks have as they is so locked down and have TPM for verified boot etc. So your statement that it's easier to "curtail games on your system" is probably false. For a brief summary, look here: https://www.google.com/chrome/... there's a whole lot more info on the detailed policies if you search for it.
3. The hidden cost and inefficient of managing your own onsite storage and backup.
You're almost spending more money than you need to managing your own infrastructure. Your cost of storage is certainly an order of magnitude higher than Google's due to their scale. You're doing backups - but it sounds like they're on site. Where's your geographic redundancy? Google will store your data across multiple geographically separate datacentres and manage all the infrastructure for you.
4. Your unjustified fear of losing control
You seem to still believe that Google is mining kid's information to serve them ads - yet Google Apps for education doesn't serve any ads. (http://www.google.com/edu/trust/)
You also seem to believe that using the cloud means you don't know who will access it. In fact Google, Amazon, Microsoft etc. all make it pretty clear the controls they put in place regarding security and privacy - and back these up with SLAs etc. I'd have a lot more confidence in their security and privacy controls than in your own IT team. This is probably most contenious area, but you could start by talking to other schools who have made the shift to see how they overcame these kind of concerns.
I get that change is scary - and there's a lot of cloud FUD out there. But I'd really suggest you take the time to understand as it is fundamentally shifting how the vast majority of IT systems are delivered. I also think that keeping on doing things how you've always done them isn't a sustainable strategy in the long run.