What would be the purpose of this diet plan?
The main cause of gout isn’t what you just ate but uric acid crystals which can accumulate in one’s joints over the years. So the main point of a gout diet is usually to reduce the amount of uric acid in one’s blood. But assuming the test result you mentionned is 3.3 mg/dl (perhaps you could double-check both the number and the unit with your doctor’s office), that indicates a very low amount of uric acid already!
Now because these crystals accumulate over the years, it’s possible you might be suffering from gout even though the amount of uric acid in your blood is currently low. Indeed gout pain can be triggered by an improvement in one’s diet. But this type of gout is temporary. You might think of it a residue of past diets or lifestyles. The residue slowly dissolves and once the process is completed, one’s gout is cured.
I think you should get another blood test (if your last test was done only a few days ago, wait a few weeks) because the result of your last test might possibly be exceptionally low. It happens, especially after flareups.
But if the amount of uric acid in your blood is consistently that low, there is no point in changing your diet in the hope of lowering it further.
A ketogenic diet is something which might bring about uric acid problems but maybe your body can handle that well. Still, if you often carry out such dietary experiments and you suspect you are prone to gout, you might want to keep monitoring your uric acid.
But perhaps you have a goal other than minimizing uric acid such as preventing inflammation… in that case, please explain what you are trying to achieve.