Name is Greg,
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You answered your own question . if the fuel pump is needing time to get to pressure then replace the fuel pump .
What i suggest you try first to confirm this is jump the connections on the diagnostic connector as shown and wait 10 seconds (ignition switch to ON) .
This will build up the fuel pressure ,then start if the engine catches and starts up normal replace the fuel pump.
If you could redo a fuel pressure test and it takes longer than 2 seconds to get to pressure replace the pump .
After replacing the pump you have to prime the fuel pressure by jumping the system as shown above before starting .
Need further assistance then please get back to me .
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