The noni you ate looks rather different than the noni here in Hawai'i. They are typically much bigger than yours and the flesh color is much lighter. I suspect the ones here are much milder in flavor than in, say, Thailand, partly because I've read that the varieties here have much less of the putative medicinal component. I think they are pleasant and refreshing in small quantities. They are fairly sweet when fully ripe. When I happen across a tree with ripe fruit, I typically eat maybe one quarter of a fruit and enjoy it before the mild burning or bitter flavors become distracting.
The ume you ate looked totally unripe. I've eaten ripe raw ume and it's a sour, pungent fruit, but still edible and not offensive. They are sold green for making umeboshi, which is another example of something that's quite tasty in small quantities or diluted with other foods, no different than many pungent Indian pickles that are very popular. I wouldn't pop a whole umeboshi in my mouth, but a sliver of one is a sublime sensation.
It's easy to empathize with your chempedak experiences. I've only had it from 3 different trees, but I found it extremely delicious each time, possibly a top 10 favorite fruit, although I prefer jackfruit. As much as I enjoy it, I agree it's extremely funky. It's the only fruit I don't like to leave sitting around on the kitchen counter all day. I like the smell, but prolonged exposure to it is overwhelming. On the other hand, I routinely leave durians sitting around on the kitchen counter for days and barely notice the smell.
The worst fruit I've tried is cannonball. I let it ripen for a few weeks--the smell is really intense too--and I was confident it was ripe but the oxalic acid taste was still too strong to enjoy it. There is a sweet creamy flavor in there, but overall its edibility is questionable. I'd put bilimbi in the worst 10, but only because I basically like everything and I only like it a little bit. The flavor is okay, kinda boring, but it's so extremely sour that I usually avoid it eating it out of hand. Similarly, rambai makes my worst 10 because even though the sourness is easily tolerable, the other flavors are too boring and bland to balance it out. I've tasted it from 3 different trees and I'm sure I had it at optimal ripeness and a reasonable sweet/sour balance, but I would generally prefer a sweet, cheesy noni over a rambai.
