I'd be inclined to ask for a discount off the labour as opposed to the goods. What portion of the 27k was for the labour? I'd be willing to pay for the goods but I wouldn't be paying for the labour (or perhaps only a portion of it).

Regarding the youtube, leaflets. Not a great solution. May end up with a defamation action against you which would be a major pain. I think a better approach would be to put your complaint in writing to get the wheels in motion and to have a look at a fully itemised quote so that when you ask for a discount it is clear and precise.

HTH
Spring

ETA: Also great idea to take photos. Just because you have another kitchen you can use doesn't change the fact that the delay is unacceptable. What if you didn't have another kitchen????