Dispute with BG ongoing since February

I’ll be as clear as I can with this, but there are so many channels going on it’s starting to get blurred.

So we moved into our new place in February, we decided to close our account with British Gas where we had an outstanding balance of £573.88 - I can’t remember the initial reason why we were offered our first compensation of £100 but I think it was down to conflicting information provided by the staff at BG.

The complaint handler reduced our bill to £473.88, we asked to set up a payment plan as my wife was due for an urgent operation where we had to pay upfront. The complaint stated to us we cannot set up a payment plan so we chose to resolve the complaint as we get like we had no further options.

A week later I received a phonecall from BG, asking if we could advise the method we could pay our outstanding bill and if we wished to set up a payment plan. I of course lost it, as we were advised we could not set this up - so we opened up another complaint.

We received a further phonecall, asking how we could resolve the complaint and I requested a further £100. Complaint handler on the phone advised this had been accepted and bill reduced to £373.88 providing we could give direct debit details and set payment plan up. We provided this and assumed this was set up.

Few weeks later we were then advised over email they could only apply an additional £50, and they are waiting on our account details to set up our payment plan. There seems to be no action taken regarding our last phonecall. Since this I have straight up refused to talk to BG over the phone, and I now require everything in writing over email.

BG are not confirming the extra £100 has been applied so our bill reduces to £373.88 - each email we have received since is ignoring that we had telephone confirmation of this.

I’d like advice on next steps now. Learning what kind of company BG is, I’m hopeful all phonecalls have been recorded - but it wouldn’t surprise me if they have no recordings. I have emails.

Should we accept our deadlock letter and let the ombudsman review this? I feel we have a good case, dependent on the evidence provided by British Gas