My opinion
Claimant requested a change and a change was proposed, the question is did the quote mention any change had been made and the claimant would be required to confirm or reject the cost? Maybe it was emailed but not explained hence why BA accept they made a mistake?
In either case by error or on purpose, BA cancelled the contract, them accepting it was done in error however it does not change the legal position, that the contract was cancelled by BA and any refunds would be provided in line with the typical T&C's.
BA offered to remedy the situation, again they would argue as good will, given no contract is enforce a proposal was made and the proposal was rejected. Your entitlement is legally based on the contract a partial refund, however expecting BA to offer the difference a judge would say is unreasonable. BA would argue on the basics they offer to travel you from A to B, they offered an alternative class and offered to compensate. They were unable to offer the class you requested and I assume you needed to fly in the date requested as oppose to a day later. Given EU261 does not apply your in uncharted territory and working on common law basis where class of travel has level of a value.
BA would either as good will agree to refund the amount if they choose but have no legal obligation, if they opt for a partial refund they are applying the contract or law. Your argument for same class could work on a common law basis where the argument is it’s unreasonable for person of your stature to be in an lower class ie footballer, known ceo.
It will be interesting to see how this ends, good luck!