Your offer was more than fair in my view. There are rules about backdating bills which say, for example, that for a domestic supply, if no bills are issues for a period, the next bill should not go back more than 12 months. If the mix up was due to the supplier's mistakes, I would have dug out the exact wording of the rules (the rule I'm thinking of is where no bills are sent for a domestic supply so it's a guide rather than something applicable to you) and started with an offer of one year's usage.
I approached the Energy Ombudsman a few years ago and they were not interested in my situation. I questioned their decision because I felt my situation fell clearly within their remit but they just sent a couple of standard letters saying otherwise. I was not impressed and I got the impression that they work for the suppliers who provide funding rather than consumers. Other options include Consumer Direct / Consumer Focus who are going to be reorganised shortly and so staff may have other things on their mind.
My feeling is that, if you are offering £17000 and EdF are asking for £21000, then you are fairly close to agreement and you should continue to negotiate. You can change your offer slightly by proposing, for example, three annual payments of £6000 but you should make it clear that you feel that you are being more than generous by offering to pay for 4½ years of gas when certain rules in other circumstances where the supplier's billing is at fault would restrict backdating of energy bills to 12 months. You can also state that, because your £17000 offer has been rejected, you are now under no obligation to make the same offer again.
It would be best to communicate by letter as it is not unknown for suppliers to "lose" their record of phone conversations when it suits them.