Low oxalate and low carb do fine together. You might want to look into the carnivore diet, even: no oxalates at all in that, nor carbs. That actually gave me kidney stones (ureum stones, not calcium-oxilate ones, are my problem), so it could well work miracles for both your blood sugars and your kidneys. Just remember to, whatever type of stone you have, drink enough. Flush out as much as you can, unless you suspect a blockage.
Good luck!
Jo
PS: I take it you're not just assuming "probably oxalate stones" because they're more prevalent. Yours did get tested for type?