British Gas Business - contract and backdate issues. Any advice?

Hi all! My business moved into a premises on 1st January 2019, and have had an ongoing issue with British Gas, which has taken over ten months to solve. The problem was on their end, in that the meters were showing as de-energised and/or not linked to the correct property. The solution they have now offered is totally unsatisfactory, and I wanted to seek any advice on what grounds I have or what I could legitimately expect from them.

The basic and impartial facts are as below:
• We moved into the premises on 1st January 2019;
• I first contacted BG on 13th February, seeking a deemed rate bill to 13th January and a backdate of contracted rates from then to 13th February, followed by a contracted term (30-day rolling) before being able to switch to a cheaper, renewable provider with excellent customer service;
• It turned out that there was a legacy issue with one of the meters, which has taken to November 2019 to sort out;
• The delay in getting the backdate sorted hasn’t been our fault;
• In the interim, I have spent the equivalent of multiple days on hold to and on the phone to BG in the last ten months, trying to sort this issue out, costing our business in terms of my time as I’ve had to repeat the whole back story to various different customer service agents;
• These calls cost money, as well as time;
• Upon getting this sorted, we are offered a backdate to 13th February (not 13th January, which it should be at the very least, as they offer a one-month backdate as standard), but would be required to sign up to at least a one-year contract, as contract lengths have to be at least as long as the backdate;
• (To reiterate) the length of the backdate was not down to our error or omission, rather BG’s;
• The contracted rates we have been offered, in any case, would be at least £137 per year more expensive than the other provider, whom I would have switched to on 13th February if BG had not encountered the issue;
• We’re already going to be liable for approximately £100 more than we would have been had we switched, for the time we have already been in the premises.

The solution and compromise that I have offered and would accept is as follows:
• Ideally, as a gesture of goodwill and to compensate us for the time wasted resolving this matter, we are able to backdate to 1st January, and pay the contracted rates for the period 1st January to the present date, us accepting that this way, we’ll be liable for about £100 more in total than had we originally been able to switch when planned;
• If this isn’t possible, at the very most, I would accept paying the deemed rates for the period 1st to 13th January (I have meter readings taken on 14th January), and then the contracted rates from 14th January to present;
• With BG accepting that the backdate was not our fault, we are allowed to switch provider straight away once the bill to date is cleared, or at the very maximum, are put on a 30-day term after which we could switch freely.

So, while I think I've been reasonable and very fair in what I'm seeking, does anyone else have any similar experience or advice? I'm awaiting their response to an email now, but seeking guidance in the meantime.

Thanks so much in advance!

Jack