There is loads of research that clearly demonstrates that it is high carbs in diet that elevates Trigs and reduces HDL. I am sorry, but I am not the sort of person who makes notes of references as I read every piece of research, but in recent years numerous studies that were originally set up to demonstrate that Low Carb diets are harmful have demonstrated the opposite, certainly in terms of Triglycerides and HDL. LDL usually stays the same, or reduces on LCHF - but for a minority of people it rises. In some, that rise will be temporary and drop back after weight loss ceases, but in some, the LDL stays 'worryingly high' if you believe the Cholesterol / Heart hypothesis. If, like me, you think the Cholesterol / Heart hypothesis is a load of rubbish (good job really or with an LDL over 7 I'd be running to the Statin shop and turning vegan!) it's irrelevant, because with high HDL and low Trigs my LDL particles will be of the 'large fluffy variety'.
The Framingham Study, well published, in peer reviewed journals, in further investigation by independent scientists has been found to misrepresent the conclusions and exclude data that seemed to indicate the opposite to what they had hoped to demonstrate, a clear example of cognitive dissonance. It would seem that the original researchers of this huge project had no conflicts of interest, they just couldn't accept their own findings, such was their conviction that the Cholesterol / Heart Hypothesis was correct.
With so many high powered medical journal editors (usually on their retirement) expressing grave concerns about industry bias in research and the total failure of the peer review system in medical research (it simply confirms the existing bias, reviewers virtually always have established their reputation on the existing theories, research that challenges those positions is much harder to get published).
If you have an open mind, I really recommend you read Nina Teicholz's 'Big Fat Surprise' and Ben Goldacre's 'Bad Pharma'. Both are well researched journalistic accounts of how science has been perverted over many decades, often putting profits (and egos) ahead of people.
I suspect you are wedded to the Cholesterol / Heart hypothesis, fair enough. Only time will tell who is right in the end, I suspect most of us won't be around to see the final, conclusive evidence, if there ever is such a thing. Correlation does not prove causation - and long term (over decades) interventional trials on diet and health can never be conducted.