I'm afraid that they don't do readings in between their normal ones - for any reason.
When I first came out to Spain and became an Estate Agent here I could not understand why we spent so much time getting previous bills and calculating possible liabilities for clients, until I was told that you cannot get final meter readings from anyone.
It is completely nuts, but that is the way they do things - certainly here in Orihuela Costa!
You should be able to do your own meter readings as the elec meter is usually on the wall of the property and there is a glass window, even if you don't have the key. Our water meters are kept shut with a little bit of wire, but your President may have the key if yours are locked. You would then have to do your own calculation but the unit rates should be on your previous bills.
Good luck!