Yes, there are dozens of issues with CR and some involving Refunds recently mentioned in this forum. I would be good to think more exposure, or as I would prefer transparency, would help but the reality is that Customer Relations has a backlog approaching 6 months on some cases. So bad that some complaints can no longer be properly answered since the relevant data has been archived.

Now there are 3 parts to your question and I think it's helpful to deconstruct this issue
- the complaint / customer relations side. This is the worst area, and before making a complaint it is sometimes best to simply not to so. Why? Because the refunds team is separate and nothing like as badly overloaded (though they are busy). One process is you complain, CR finally reads your message, then kicks off the refund process - this takes way too long, and in the last 3 months I have seen no improvement. Status passengers can sometimes get considerable priority here.
- refund for the fare difference - as noted above you are entitled to more that under Mennens. But if you just want that fare difference refund, then it can be expedited. This is because the Engagement Centres can contact Refund and escalate there, as well as see Refund processing. Whereas the Engagement Centre cannot contact the Customer Relations team and cannot see what they are getting up to (though usually it's nothing at all so they could guess). Within Refunds there are various queues internally, and sometimes a BA staffer will say "the refund has been processed", when it actually means "your refund is OK for refund, and it now goes through a few hoops and within the next week or so it will leave BA and arrive at your credit card. Then your credit card company may well take a while to show the refund". Amex, incidentally is by far the fastest refund route since Amex shows refunds within hours.
- Mennens - this needs specialist staff and will take a while since it is a relatively complex calculation. Many FTers find it difficult to work out even with the worked examples in the wiki mentioned above.

You could just go for the technical refund and then separately apply for Mennens after you have had the fare difference refund.

I wouldn't let it get to you since you really can't change it, no-one can. Just be patient and at 8 weeks go to CEDR. If you can work out Mennens it may be better to go MCOL since the courts impose deadlines which BA is forced to meet. One deadline relates to the preparation of defence documents and they can't easily say that you are not entitled to the refund.

I too had considerable problems with a very small refund (£110) recently. BA cancelled the flight, and thanks to Nexus I was only given a voluntary refund rather than involuntary one. This meant BA charged me £15 for the privilege of BA cancelling their flight! The first attempt of the refund claim got deleted in error, the second attempt was denied because the refund had already been paid (the refund agent didn't read the notes in the booking), after the third call to Refunds the £15 was paid but not the rest, the fourth call "it's been escalated", fifth call "the payment process should start tomorrow", which it finally did. And that's with someone who knows how to navigate the system.

I came close to doing a chargeback on this, which I guess is your other option here, if you are able to work out the approximate maths. Just round it up by £10 in your favour to annoy BA.