The accumulator maintains pressure for a restart......typical symptom of accumulator problems is needing a couple of tries when restarting after sitting for a while

Dry pump would come from lack of fuel supply to it....I noted what I called 'zinging'......speeding up of pump....and the groaning as it tries to catch up

Anyway I'm sure fuel delivery measurement is the key to diagnosing your problem

You should be able to get a new fuel pump for alot less than $300 in the US.....others talked about ~$US160 in a previous thread