You mention "estimated" months, but my experience (with only one utility company) with something they call budget billing is that they divide predicted costs across the 12 month period, but still read the meter every month. Each bill shows how much I used (kWh) and what it would have cost, then they deduct from my bank account the amount that was budgeted and then show the "net balance" in the budgeted amount.
You make a couple of statements I want to comment on:
It seems as though they are back billing me (which should be a one
time thing), but then going straight back to "estimating" usage at
this new (higher) rate.
If they are doing their version of budget billing and it works the same way as with my account, then every year they should re-calibrate the monthly amount to account for what was used over the 12 months. For example if at the end of the 12 months they under estimated by $200 total they account for the under charge by spreading it over the next 12 months at $16.67 per month and bump up the budget amount by another $16.67 because they have learned that I use more electricity than they originally guessed.
The initial high demand when I moved in seems like I was paying for
someone else's (or the empty unit's) "estimated" electricity usage,
which was then piled on me when I moved in!
According to my local utility company you wouldn't even be eligible for budget billing:
You must have at least 12 months of billing history at your current
address and must not owe more than your current bill to enroll. This
means if you were a little short on a previous bill, it must be paid
before you can enroll in budget billing.
That would mean if you moved into a place, they would prevent you from using the budget billing plan for 12 months; otherwise your estimate would be based on the previous occupant.
It is normal to see a spike on the first or last month, because the meter reading isn't in synch with when somebody moves in or out of the apartment.
It isn't normal to have multiple months of "estimated" readings. Decades ago an estimated reading would have been a simple calculation, they probably would have just looked at the usage from the previous month. But now they take into account days in the billing cycle, average daily temperature, and the fluctuating cost of electricity generation and give you a better guess. So even if they were skipping reading, the guess would change each month.
I would talk to the utility company, and the management company of the complex to understand how the usage and bill are being calculated. Some utilities have one meter per unit, others one meter per building. You want to make sure you understand where they are getting their numbers from.
