Your system fails immediately when prices rise. Since prices rising is inevitable, your system will inevitably fail. Even if it did work for a year, you hit diminishing returns right-away, and there goes the motivation for further/continuing effort.
This is a problem that cannot be solved by playing with numbers on a spreadsheet. Group rewards don't promote individual responsibility because the benefits of individual sacrifice get too diluted. Only individual meters will promote individual responsibility.
The root of the problem that you are trying to solve has nothing to do with the tenants — the problem is with the landlord.
Landlords are, by definition, rent seekers. They want passive income for minimal, preferably no effort.
As long as the landlord can just 'pass the buck' down to the tenants (i.e. get them to pay all the bills, regardless of how large those bills get), they will do so. They don't care about responsibility. They don't care about fairness. They don't care about the environment. They just want profits. And they don't want to spend a cent or lift a finger to collect those profits.
Installing individual meters is entirely possible, and not even that expensive (especially for only three dwellings). But what motivation has the landlord got to install such things as long as he can legally force the tenants to pay the bills? Absolutely none. The bills don't affect the landlord so the landlord doesn't care about the bills.
Your only hope of solving the problem is to make the landlord care about the bills.
Since landlord rights are enshrined in law, that would most logically be what needs to change in order to solve the problem. Good luck with that. Once rackets are sanctioned/protected by law they are incredibly difficult to dismantle.
In this day and age, perhaps a more appropriate way would be to publicly shame landlords into action? Create a website which acts as a register. People from around the world could report that their dwelling has a shared meter and, as a result, they are stuck paying huge bills because their wasteful neighbours don't take any responsibility for their utility usage.
If such a register became widely known and used/checked then dwellings with shared meters would see their occupancy levels drop over time. This would affect landlord incomes. This would make landlords care about utility bills. Landlords would want to see their properties removed from the register. This would prompt the installation of individual meters. This would solve the problem.
Tenants could scan/photograph a utility bill and upload it to the website, along with the address details. The website operator could quickly view the bill to verify that the bill is a shared one and that the address matches the one provided. Click a button and bang, the address goes public and appears on the register.
If you make it free to report dwellings with shared meters, many disgruntled tenants will do so. If it becomes a popular place for would-be-renters to check, then traffic levels will be high, so ad revenues could cover or exceed the cost of hosting. Submitted scans/photos need not be stored on the website — they could be down-/off-loaded and archived so they don't count towards storage quotas. All you need to keep is an address. Less than a 1 kB per dwelling. Very minimal setup, very cheap as far as running costs are concerned. World-wide scope.
The internal (or even public) project name could be the Shared Meter Register (ShaMeR)... ;)
Anyway, Yelp is based on a business model of publicly shaming companies that provide bad services. I see no reason why crowd-sourced reporting can't be leveraged to shame landlords into installing meters so that tenants receive the information they need to be more responsible in their utility usage.
I realise that none of the above actually answers your question, but I do think that the problem you have highlighted is a very important one — affecting many, many people and consequently having a noteworthy environmental impact — so it is worth discussing and finding a solution for.
If your question was more generic (e.g. 'Shared meters do not encourage responsible utility usage — how can we change that?') then perhaps the net could be cast wider and more potential solutions could be presented?