I have a 2003 Toyota tundra with the 5VZ-FE engine. Never had an issue of this kind, but I’ve done some research into these engines and I can provide some advice. Yes, your issue does indeed seem to be isolated to fuel pressure regulator and/or fuel injectors. Should you need to replace them, your intake manifold needs to be removed. I will recommend what else you want to address since you’re there, but let me expand more into your fuel injector replacement procedure. Please keep in mind you’re dealing with gasoline and make sure you have a clean environment free of sparks and well ventilated.

• If you have money to spend, definitely go OEM, but midwest performance has a set of reman denso injectors for a fraction of what they cost anywhere else (thank you, timmy the tool man). Google midwest performance 5VZ-FE denso injector set. These do not come with the seals, so keep that mind. You can buy these seals anywhere, but Rock Auto is your firend here.
• For your fuel pressure regulator, yotashop is your go-to. Also you may find good parts on Rock Auto. I highly recommend you change the crush washer too (its a banjo bolt set-up scenario).
• While your intake is out, inspect it for cracks. Check all the vacuum hoses. Since you’re there, replaced them all. They’re 20 years old and once removed, they may never seal the same.
• Check your upper and lower intake plenum. Inspect of cracks and other issues. They’re aluminum so if something is amiss, it is hard not to notice.

Now, since you’re there portion and assuming these have never been done before:

• While your intake manifold is out, the v-valley of the engine will be exposed. These engines have a heater bypass tube that runs from the front of the engine, to your heater core. Over time, the sealant used to seat this tube to the engine will become brittle and cause coolant to spill into the v-valley of the engine. Highly recommended you pull the tube out, and reapply Toyota black RTV gasket maker to ensure this leak never occurs.
• Replaced your intake manifold gaskets with a high quality gasket set. I used a good set of Rock Auto when I did mine.
• Knock sensors and knock sensor wiring. Let me put it this way: if you have everything apart and put everything together without replacing these sensors, you will HAVE to take everything apart just to replace these sensors when they go bad. And they will go bad. If you opt in to not replace the sensors, at least replace the knock sensor wiring. Google it and you will see yourself.

Thats it. I hope you have this issue resolved. Should you need anything else, feel free to DM me.