wa'Hu' jIghungchoHDI', pItSa' vIvunpu'

In the sentence above, wouldn't it be preferable if instead of {jIghungchoHDI'} we had {jIghungchoHpu'DI'}, since we report an event by looking back on it?

Only if you're reporting a completed act of becoming hungry. But that's not necessarily the function of jIghunchoHDI' here. You might be instead be talking about something happening at the moment the change to being hungry occurred.

It's the difference between "Earlier, I wasn't hungry, and then switched to being hungry. Once this change was complete, I ordered pizza" (with -choHpu') and "Earlier I wasn't hungry, then I switched to being hungry. As this change occurred, or just at the tail end of this change, I ordered pizza" (with only choH).

Which one you use depends on which story you're telling. The version with -choHpu' is probably about how, because you became hungry, you ordered pizza, while the version with just -choH might be about how your hunger and dinnertime happened to coincide. There might be other reasons to choose one or the other.

And returning to the question troubling me earlier, I still have this problem which drives me crazy:

Regardless whether we write {wa'Hu' jIghungchoHDI', pItSa' vIvunpu'} or {wa'Hu' jIghungchoHpu'DI', pItSa' vIvunpu'}, can't this be understood as "I have (already) ordered the pizza, before I become/have become hungry"?

Saying wa'Hu' jIXpu' doesn't mean "as of yesterday I have already done X." It means "yesterday, I performed a completed action X." "Completed" doesn't mean action X was a fulfillment of a goal; it's just a way of looking at action X from afar, without internal parts. If I say Yesterday I ate dinner, that doesn't imply that I ate everything on my plate or that I stopped when I was no longer hungry; it's just a way to describe the eating from a temporal remove, in its entirety without internal detail.

-- 
SuStel
http://trimboli.name