It does not appear the AZ are shipping vaccine to customers based on price. We know that Pfizer are, which is why Israel has been able to pay them a premium to get vaccines first.
Rather, AZ appear to have set up manufacturing dedicated to particular contracts - for instance separate manufacturing in the EU, manufacturing in the UK, manufacturing in the US, and manufacturing in Latin America. They seem to have written contracts that say 'you get what your dedicated manufacturing produces'.
The dispute between the EU and AZ is about whether the UK counts as being in the EU - in my opinion AZ appear to have taken money from the UK to build factories there, included those factories in the EU's contracted dedicated manufacturing when they should not have, and then refused to give the EU the vaccines from these factories.
This became relevant because AZ manufacturing yields are lower than expected - less vaccine than expected is being produced for a given amount of manufacturing capacity - so the bugs in their contractual arrangements have become visible.
So, I agree that AZ screwed up, but I disagree with your model of why.