Guppy, that is long and passionate, and raised far more issues than are in the question. You were presented with a simple medical emergency scenario with a weather problem. Everybody has been making far more of it than the problem presented. The lesson to those trying to learn is forget about heart transplant issues when they don't exist in this problem, handle the immediate problem, remember what limitations are for and always consider the safety of all those on board. It leads to one answer! With UK ATC (at least), unless you declare an emergency, you will get no preferential treatment whatsoever. You may expect few, if any, countries outside the UK will even recognise the term 'pan-pan' or know what you are talking about. Therefore to have a severe medical condition on board, the only option is to declare an emergency.
In practice, I had such a transatlantic condition this year. With proper communication, I received full co-operation from ATC without having to declare an emergency, and was fully satisfied with the handling.