You might be pleasantly surprised on your cholesterol levels when eating less carbs and more fats.
All my lipids greatly improved over the last 5 years, and I eat more fat than before, including lots of butter, cheeses, pork belly, eggs, things like that.
And again, eating stuff you don't like is a good way of setting yourself up for giving up on your chosen diet.
If I were you, I'd focus on blood glucose first, and leave everything else for later, unless something unexpected happens like lots of weight gain or such.
For one, it's less overwhelming, an secondly, both weight and lipids may improve all by itself with the improved diabetes.
Please see if you can get the extended release version, many people report a lot less side effects!