I used the standard lexical sets in Wells' Accents of English series to try to figure out which vowels could be allowed into an IAL.  For those who are unfamiliar with this stuff, there are 24 lexical sets plus another 3 (sometimes 4) for final vowels:

I put RP up against GenAM and I needed a representative of Caribbean accents so I chose Barbadian which hooks into GenAm nicely and seems to be the best choice.   I found that all but 5 lexical sets could be allowed through, on the basis that they have to be mappable to one of the three accents, so that it is easier to list the ones that I would NOT allow through:


This was a useful exercise for me.  For example, it explains why I would not allow WAN for "one" (it is in the STRUT lexical set).

I must admit I find it hard to see how I would use some of the lexical sets, eg. THOUGHT, CHOICE in practice, but I have not ruled them out.