High triglycerides can suppress HDL, and are associated with high VLDL. Also, high
carb and
low fat is what causes the preponderance of small dense LDL.
The wine might help raise HDL a little bit, but will raise triglycerides even more. I'd ditch it, even though moderate alcohol is generally cardioprotective for most others. I am not a low-carb dieter myself by any means, but it's uncanny how the low-fat / high-carb seems to be going wrong for you.