Fuel pressure

The hard restarting is likely due to fuel pressure dropping to 0 psi. The pump will run for one second when the ignition switch is turned on, but that isn't long enough to build pressure from 0 to 45 psi. The pump doesn't resume running until the Engine Computer sees engine rotation, (running or cranking). During cranking, battery voltage is drawn down a lot by the starter, so the fuel pump will run slower than normal and take longer to build pressure. You can overcome the hard starting by turning the ignition switch to "run" without cranking the engine. Wait for the pump to time out, turn the switch off, wait a few seconds, then turn it on a second time, then crank the engine. Do that even a third time if necessary.

There's three places fuel pressure can bleed off. The least common is through the check valve in the fuel pump. To identify that, while the pressure gauge is attached and you see the pressure dropping, use a hose pinch-off pliers to pinch the fuel supply hose where it transitions from the body to the engine. That's the larger of the two hoses. If pressure holds, suspect the pump.

The second place to find leakage, also not real common, is the fuel pressure regulator. To identify that, pinch the smaller fuel return hose. Also look in the vacuum hose attached to the regulator. If there's fuel in there, the regulator is leaking fuel into the intake manifold.

The more common place to find leakage is from a leaking injector. There's two ways to find that. If you are able, on some engines you can remove the spark plugs and look inside the cylinder for dripping gas, a really wet plug, or use a bore scope to look inside. Any fuel leaking there has to work its way through an intake valve, so it might not show up on the first round of tests. The other way is to remove the injectors, still clipped to the fuel rail. If you don't see one or two of them wet on their tips, turn the ignition switch on for a few seconds so the pump can build some pressure then check the injectors again.

Unlike some other manufacturers, Chrysler has extremely little trouble with injectors, but when you do find one leaking, they should all be replaced as a flow-matched set. That's the way Chrysler buys them from Bosch. If you just replace one or two, they could flow a different volume, resulting in misfire fault codes where you can't feel the misfires, and they have an elusive cause.