Well, my wish to eat a fresh feijoa has come true. They're just at the beginning of their season (harvested in fall), and I found a few at the store a few days ago. They're not exactly perfectly ripe, but Sarah P-C picked out a couple that were mostly ripe that I could try.
SO - here's what you do - you slice the fruit in half (how come I didn't take a picture of the whole fruit?) as in the top picture. Then you scoop out the flesh and eat it - resulting in the last picture, just the skin.
If you need yet another reason to come to NZ, come to taste feijoas.