Linky you are stating pretty much what fascinates me about your case.
Gotta be honest and I know others here smarter than me are perhaps sensibly not stating publicly. But so far I am getting the feeling that consumer rights are very poorly enforced in France. Particularly in the case of formerly nationalised (ie government-run history) industries. Of which EDF and other companies in that industry, seem a likely case. Where the industry is judge and jury and can misbehave or shrug their shoulders and put the onus on the consumer to move mountains to challenge them, they are not going to accept any fault till conclusively proven. And maybe not even then.
The French blood scandal comes to mind about how long that took to prove the challenge against the authorities. And that was a mass problem. So what chance has the individual got to challenge a formerly state-run industry that is still thinking that same way?
Either someone is using your electricity or you’ve got duff equipment - yours or EDF’s.
I’d try to find out what qualifications or agrementation a specialist has to have that would have to be accepted by EDF if that specialist states something is EDF’s fault. You say you’ve had your own installation checked. I think you’re going to have to pay again, but only the right sort of specialist EDF would be obliged to listen to. Very few months of the current overcharging would be equivalent to their costs.
If it was me I’d pay a subscription to Quechoisir.org and use 1 of the 4 legal advice calls they give you per year, to get legal advice and ask the above. I’d want to take advice about how to write something that will ensure EDF has to pay the costs of your specialist, at a minimum, if you are found right and the fault is with any part of the EDF provision.
You’d best write up a timeline of all actions and communications between you and EDF to quickly send to the assigned consumer legal person. This will also likely best be attached to whatever you send to EDF but take the advice on that.
Meanwhile I would absolutely be following Badger’s advice.
I personally can’t wait to see how this turns out whichever way it goes.