Their decision is not final, in the sense that you can appeal to the UK Small Claims court. However any CEDR judgement may be pushed strongly by BA if it went against you. As to whether they are fair, it's a bit of a mixed picture. On some judgements they can be inconsistent between 2 very similar cases, and we can't avoid the simple fact that BA funds CEDR, it's cannot be truly independent. On the other hand, particularly on the "all reasonable measures" aspect of EC261, CEDR has a good record of settling on the side of the consumer.

In your case, firstly welcome to Flyertalk, and it would have been better to raise it here as soon as you hit the problem. But even so, in the absence of details, that your claim is rather large, and that probably it's not been processed correctly under APR. See the EC261 / APR thread for more information on that. By all means make a new claim, or ask that it be reviewed by an APR specialist, but (without knowing more) it may be best to get this down the CEDR route as soon as BA has confirmed that their answer will not change.