I think on some of your codes since this is becoming an OBD mess you are going to want the full five digit code specific code, not the four digit code the generic readers give. Might be worth calling a dealer and talking to the service writer.

Gotcha. I'll call them today.

Fuel Pressure Issue, Hunting and Sluggish Acceleration
 

I took the car to a classic Jaguar Specialist. He seems very well respected, he actually worked at the factory back in the day. He scanned my codes and took the car around, didn't even charge me. Apparently I have a bad gas cap, so I've ordered a replacement. He told me my fuel issue was almost definitely a Fuel Pressure Sensor. According to him the part is a bad design and he's gone through several before finding one that worked on a couple of cars before, so I took My car home and ordered a new one. Swapped it out and no dice. Something hit me the other night, could the car be putting itself into Reduced Performance mode and not telling me? That could explain why a battery reset would improve things and why initially restarting the car would "Fix" things". I'm beginning to suspect that a bad fuel filter could be the cause and the car is cutting performance to protect itself. Does that sound plausible? If I can figure out how to depressurize the system I'm gonna try replacing that tomorrow. The Shop Manual wasn't much help on that.

Whelp. Put a new fuel filter in tonight. Now the fuel pressure reads 46 even with an occasional dip to 45 instead of being all over the place. Looking like it's the pump. Replacing that thing looks like a beast of a job.