My total cholesterol definitely went up since going Primal. However, it's because my HDL's doubled. Red meat probably won't increase your TC because stearate has little effect on cholesterol. Coconut oil may increase your TC significantly, but it's almost always at the expense of HDL's going up.
Also, how do you know it's due to saturated fat? Did you drastically drop your carbohydrate intake and increase overall fat intake? A higher fat intake is probably going to raise your total cholesterol. It doesn't matter as long as your ratios are good. Lowest all cause mortality is lowest with a TC of 200-240. A doctor will tell you you have high cholesterol. Not so according to actual mortality facts. If you want bad cholesterol, go <160 TC. Funny thing is a doc will give you a gold star.
Cholesterol IMO is one of the least useful tests anyway. What do I consider far more important?
Estrogen / Cortisol / Adrenaline
Cholesterol doesn't tell you a whole lot. I want metabolic health. Chances are someone with a properly functioning thyroid, a strong CO2 reading (indicating strong mitochondrial oxidation), low estrogen/adrenaline/cortisol, high testosterone, stable blood glucose (73-80) and low c-reactive protein has a healthy metabolism and low inflammation. You're probably not going to get heart disease if you're not inflamed, your stress hormones are low and your metabolic rate is high regardless of cholesterol, right?
Trying to correct your cholesterol when you're an inflammatory, stressed out mess is like wearing a bulletproof vest into a bad neighborhood. Why not just stay out of the bad neighborhood?