Those readings after meals are very good - look at the actual rise from before to 2 hours after, they are very acceptable rises, and the end results are all within range. It is your starting levels that need to come down. The higher you start, the higher you will finish.
The NICE guidelines for type 2's say between 4 and 7 pre-meal, and under 8.5 2 hours after. However, these are a little out of date and too generous in most people's opinion. Some of us are aiming for non-diabetics targets, which according to NICE should be between 4 and 5.9 before meals and under 7.8 at 2 hours.
I have lost 3 stones 3lbs following a low carb diet with increased fats - I just ditched the low fat products and changed back to real butter, real yogurts, real mayonnaise, and stopped being afraid of things like bacon. However, I don't go overboard with the fats, I just don't actively avoid them. As said above, if you drastically cut the carbs you have to increase either the fats or the protein or you may make yourself ill. Just keep an eye on the calories.