I'm in the same boat and switched to Aeropress. It has marginally reduced my cholesterol in 3 months. My diet didn't change significantly in that time except that I started eating oatmeal regularly in the morning instead of granola. So totally unscientific, but I'm going to continue with the change.
Just be sure to use the paper filters and not the reusable metal ones. Only the paper filters remove the oils responsible for raised LDL.
A side benefit is that Aeropress coffee tastes great! I highly recommend it.
The thing is, I fear I like the coffee oils I get more of with no paper-filter. I assume it’s one of the reasons French press is my favorite method of making coffee.
You can test this hypothesis pretty easily since coffee oil is a surfactant. Get freshly roasted beans (ideally less than 2 weeks) and make your French press. Once the brew is ready, skim off the foam on the top and you will have removed a significant amount of the oils from the coffee. Be sure to taste blind, ideally using the triangle method.
Edit: see also the studies about cafestol being strongly correlated with lower risk of renal cancer. This is a very complicated subject and the analysis of it should be done in concert with real medical professionals.
"There’s no significant connection between coffee and increased risks of heart disease and cancer."
And, by far the most important quote: "Talk to your doctor to about any concerns you have."