All good advice.
1 check accumulator pressure. 5 psi is OK, but often when you use a guage, you release too much pressure. give it 5-10 pumps with a bicycle pump--no more.
It is possible to have a split diaphragm
in the accumulator You will know this because water will come out of the schrader valve.
There should be a check valve on the feed-in side of hot water service
and you need to check that this is working. There is also a check valve between the pump impeller and accumulator but if this is faulty the pump would be operating at times when no-one is using water.(cycling on and off)
The working principle is that the pump accumulates a volume of water in the accumulator which then is pushed by the extension of the diaphragm away into the water supply.
If the flow is low then the pump will stop working as the accumulator releases water. Think of the accumulator as a bagpipe bladder. The piper is pushing air into the bladder as well as pushing air out into the pipes. In your system something is not working and the bladder (accumulator) is not maintaining uniform pressure.