2004 XJ8 starts fine when cold. Had check engine lite (solid) for months. Got a code reader and the codes are consistant: P0300, P0303, P0305, P1316, P0128 and P1111. Car was still running with the codes until recently. Now occasionally it will stall at idle when slowing for a light or when putting it into gear after a warm start. When it stalls out like this it then will not start up again. It cranks and tries to start but won't idle and turns right off. If I let it sit overnight it will start and run until the next stall. Have replaced the MAF battery and air filter. You can hear the fuel pump run for a couple of seconds when you turn the key. Tried swapping coils and plugs for cylinders 3 and 5 with no change in missfires on 3 and 5. Any help would be greatly appreciated.

Update: Bought a fuel pressure guage and checked pressure at the Shrader valve. When running and when in the no start fault mode the pressure is steady around 50 PSI. So issue doesn't seem to be the fuel pump. Also, occasionally I have seen a display error indicating "parking brake fault." This error was happening before the car started stalling and not restarting until cold. Yesterday I was able to run in the driveway for about 20 minutes and was able to get it to stall once after revingto 3K RPM. It restarted right after the stall unlike the last time I tried this.