I must admit that this is a little beyond me and I don't really understand what you're trying to say. Do I understand correctly that you're saying the vowel in choice is the best match for the Dutch "ui" when going off of the IPA notation, but that there exists no good match in English like there is for "ou"?
I'm saying that (1) there is no perfect or near-perfect match; (2) it isn't clear which available option is the "best" match, because the three obvious options each sacrifice something different.
If you're interested in the theory:
Vowels are generally thought of as being points in a three-dimensional space. The dimensions are:
1. Whether the vowel is high or low -- if your mouth opens wide (chin closer to feet), it's a lower vowel; if your mouth doesn't open far (chin closer to eyes), it's a higher vowel.
2. Whether the vowel is front or back. The traditional way to explain this to linguistics students is to give them all lollipops. You put the lollipop on the middle of your tongue with the stick jutting out of your mouth. You can observe that the stick juts farther forward when you're pronouncing the FLEECE vowel than it does when you're pronouncing the GOOSE vowel.
3. Whether, as you pronounce the vowel, your lips are rounded or not.
Dutch "ui" is a diphthong, a transition from one vowel to another vowel. It appears to be a transition from (lowish, front, rounded) to (high, front, rounded). This is difficult for English because, in English, all front vowels are unrounded.
If you'd like to preserve the lip-rounding aspect of "ui", you need to use back vowels, at which point the MOUTH vowel is a near-perfect (low, back, xx[1]) -> (high, back, rounded) match.
If you'd like to preserve the frontness of "ui", the English FACE vowel is available, which is a transition from (lowish, front, unrounded) to (high, front, unrounded). CHOICE is a different option; it's (lowish, back, rounded) -> (high, front, unrounded). With CHOICE, you're choosing to match the rounding (and not the frontness) of the beginning of "ui", but transition into an end that matches frontness instead of rounding.
Which part of a sound is more important for purposes of matching a foreign sound to a native sound is a very interesting question, and to the best of my knowledge nobody has any idea why different languages make the choices they do. My (American) ears think the MOUTH vowel is the best match for Dutch "ui", even though it's an even better match for Dutch "ou". But someone else might disagree.
For an example of "differential splitting", consider that in modern English, W, V, and F are three separate sounds. In Old English, W and F were "real" sounds ("phonemes"), and V was a variety ("allophone") of F. In modern Mandarin Chinese, W and F are also phonemes, and V is an allophone of... W. Clearly, if you speak modern Mandarin, what's important about the V sound is not the same thing that would be important if you spoke Old English.
[1] Rounding is less obvious for low vowels -- a certain amount of lip rounding is induced by opening your mouth so far.
That was actually very interesting! I understand what you are saying now (admittedly I first thought "more theory? Not sure", probably because I had a very hard time following your last comment). I actually get it now and feel like I learned something new. Thanks for that write-up!
As for
> My (American) ears think the MOUTH vowel is the best match for Dutch "ui",
I personally stand by my choice of the CHOICE vowel also after reading your comparison of the different options, but it's definitely a close contest.
W, V and F are also separate sounds in Dutch, but much closer to each other than in English. Wat, vat and fat are different words. The Dutch W is not bilabial like the English W, but just a "softer" version of the V. (In practice, V is often pronounced almost the same as F).
Thinking about it some more, you can get more easily away with the "eh" in MEH (not the /ə/ but the /ɛ/). That way you'll sound like someone speaking with a The Hague accent, and if you're otherwise speaking English, this will most probably slip by completely unnoticed to most Dutch listeners (unlike OU or OI would).
