I never use a pad, so I can't comment about how well they work. I do have some other ideas you might try.

Where you set up your tent can have an impact on how cold it will get at night. Cold air goes downhill, so it will be coldest near water or in a low spot. Even a few feet of elevation change can make a big difference.

The ground will be different temperatures based on the moisture content and the sun exposure. I've had the best success with bare dirt that gets the sun early in the morning.

The battle for warmth takes place quite close to your skin. It doesn't matter how good the sleeping bag is (within limits), if you wear a synthetic shirt near your skin, it's going to be cold. I generally wear a thermal top at night. With a great sleeping bag, it's best not to wear anything. Experiment with different clothing combinations.

You mentioned feeling the cold coming through from the ground. I lay my fleece under my sleeping bag which helps some. As long as I'm otherwise warm, that little bit of coolness is refreshing.

What you eat makes a difference. There is no mechanism in the human body to turn carbohydrates into fat. If a person eats excess carbohydrates, all the body can do is turn it into energy or heat. I burn about 70 calories/hour while I'm sleeping. If I want to sleep eight hours, eating about 500 calories of mostly carbohydrates just before retiring has a big effect on how warm I'll sleep.

Many people say eating fat has more effect. Rather than getting into that discussion, experiment to see what works well for you.

The coldest part of the day is the half hour after sunrise. We always get up before well before first light. My son starts the fire, and I make the coffee. We get on the trail quickly after coffee and eat breakfast after it warms up.

Note: My opinions are based on past experience and haven't changed much during the last 50 years. However, I reserve the right to change my opinions without notice.