grits,
I agree that WW is head and shoulders over Atkins as a rational diet.
Try bending the WW plan to include less glycemic items like more legumes and fewer sugars while remaining equal calorically (or "pointally"


)
As you lose weight you can expect some improvement in numbers. Keep alcohol to a bare minimum...I find it's the single worst "food" for high triglycerides.
There are also meds that specifically target triglycerides if they tend to be resistant to any diet adjustments.
Probably thyrod medication is a VERY good idea if you have a proven underactive thyroid. Nothing burns calories like the addition of some thyroxine if it's in short supply.
And, of course, exercise as much as you can.