Lee,
It seems to me that you have two targets if you are to persuade the diabetes nurse that you don't need medication.
First target is to get your sugar levels right down. Second target is to find an eating regime that will keep them that way.
The best solution to the first target, especially as you have less than 3 months to achieve both, is probably to embark on a very low carb diet. Try to cut out as many carbs as possible from your food (no bread, pasta, rice, potatoes - instead substitute other vegetables and have a higher protein portion). Also no fruit juice (good for getting you out of a hypo but not for much else). Try this for a week and monitor your sugar levels at least 4 times a day (before breakfast and 2 hours after, before supper and 2 hours after). You should be able to see a steady reduction day by day in your sugar levels. Of course to do this you will have to be very aware of exactly what is the carb content of everything you eat.
Once the levels are down you can start to experiment by adding one of the banned items (like a rice or pasta dish) and see what the effect is. You will soon come to realise which foods have a bad effect on you and should be avoided. Keep a record so that you can show the DN that you are taking this seriously.
I know that it sounds a lot of fuss and hassle, but spend a few weeks doing it now and it will benefit you for the rest of your life. Diabetes is a progressive illness so you may well have to go on to meds some time in the future, but why not keep off them as long as possible while you have the chance.