Ok pelafina, deep breaths, in,out,in,out and calm down.
I pretty much know how you feel, I didn't get what I wanted when I applied for flexible working and it was all handled pretty shoddily but you know what 1 1/4 years down the line I'm really glad we reached a compromise that both parties can live with and I enjoy going to work. Just try not to get into a stalemate position just yet.
The fact they have some p/t positions is a good one, it means they are not completely against the idea. ( I work in the financial sector and the only p/t jobs are the ones people have managed to negotiate for themselves). Is it worth asking if the shift patterns for any of these roles can be changed ? I know you are not keen on the PA role but could it be potentially offered p/t or on a job share basis, as at least that way you would keep your old grade and salary.
Have you actually submitted a flexible working request, as this means that they would need to consider your request formally and if you consult the government website, then if its turned down they need to give sound business reasons.
I just think you need to try all the options you have with your existing employer as there was something in the media recently which said it was much harder to go p/t in a new job than it was in an existing company, so if you walk away from this then it could leave you with less options in the short term.
Let us know how you get on.