MerryCouthMows...
The larger measurement would, in theory, make you a 28MM. Which, you are quite correct, is impossible to get without getting something custom made. Based on the smaller measurement, you would need a 28K, which is a bit more achievable!
Brastop sells a 28K, and has these in stock and some are very reasonably. The curvy kate sizing is a bit variable, so google for review of the particular bra before buying as their are some great lingerie bloggers out there. Although it didn't suit me, I think the Emily is qiute big in the cup for a Curvy Kate
Bravissimo fails miserably, and has these
If the 28k isn't big enough in the cup, then the easiest thing to do, in terms of figuring your size, is to go up a back and try those bras which are available in a 30k (which would be equivalent to either a 28KK or 28L roughly) such as these as well as what Bravissimo and brastop have.
The reason I suggest trying the 30s is that it is relatively simple to take the band of a bra down by a size. Any more and it's a bit tricker, but shrinking it by a couple of inches is quite simple, so if you can get enough space in the cups in a 30 back, then you just turn it in to a 28.
There is a polish bra company called Ewa Michelak, which custom makes bras on request for reasonable rates and may well be able to make you something that fits well, but I would try to figure out your size based on what is available in the UK at the moment as anything custom is also non-returnable.
You must be so uncomfortable in the 34s, you poor thing!