You never said anywhere that the dealer is refusing to refund your money after describing the first stone incorrectly. In fact, strictly speaking you haven't even said that in your post above - though it may seem implied. Have you tried asking for a full refund on the basis of misrepresentation?
If they told you that the first diamond was XXX and it's not (since it's VG/G/X), you have all the grounds to ask for your money back. If they told you "it's XXX" in a way that can be documented (i.e. in writing/email), then your case would stand in a court of law.
Your specs at the top are reasonable - even too tight, as I said already. The issue here is the process, not the specs. Incidentally, if you are planning to fit things to your current setting, then external dimensions can become crucial - how crucial and which ones depends a lot on the style of the setting, but as a rough guideline anything more than 0.1 mm difference in diameter may be visible as a gap or require significant adjustment to the setting.
Let the dealer work for his money: he is the one who provided an incorrectly described diamond in the first place; it is his responsibility to come up with options that are available and that fit the original criteria (which BTW your original diamond does - other than the polish grade). Presumably you chose the first diamond among others that were available - it's perfectly reasonable to ask the dealer to come up with more than one candidate for replacement too.
You have mentioned twice a "revised GIA report" for your original diamond. Does it mean that there is a former GIA report describing the diamond as "XXX" (as opposed to the dealer incorrectly describing the diamond as "XXX")? Why was the report revised?
If there is a previous GIA XXX report, it's possible that the diamond got scratched very finely/some facet junctions got abraded, to the point that only the polish grade is affected, rather than being noted as a clarity characteristic. If that's the case, it should be possible to repolish the stone - and that is as well proportioned as anything else that they have proposed / you have found, plus it certainly fits the setting.
Edited by davidelevi, 14 December 2016 - 06:41 PM.