Define what you mean by "tippy"

Did the thing turn over? did you fall out? or did it just rock a bit -- or a lot?

While I was pretty familiar with canoes, the first time I got into a round bottom one (instead of the flat-bottom aluminum barges I had used previously) I was disoriented. That took about 30 minutes to wear off. I finally realized the thing was not going to capsize, but that it was, instead, very responsive to my movements. I simply realxed, and learned to be more economical with my moving around in the boat.

I don't know why you would want to play with the keel. This is not a sailboat with a weighted keel. The keel helps to channel the water so the boat goes straight forward. It has little to do with rotational effects. if you wanted to make a keel that would stabilize things, it would have to be pretty big. We are talking something like a foot wide and 6 or 8 feet long. And that would not guarantee stability.

Lowering your center of gravity will indeed make the boat rock less. Not by a lot, though. You can lower your seat if you wish. Or, you can add weight to the boat and it will sink a bit deeper into the water. Either way you might slow down the oscillation. I'd try adding ballast first. It costs nothing if you just get some empty bottles and fill them with water. Stash these in the boat and see if that helps.

how tight do you fit in the boat? Depending on the performance you expect to get out of this, you may want to fit in snuggly, as if you were wearing the kayak as a pair of pants, and not just riding in it. Padding that connects your body to the hull allows you to train your boady to use the balance mechanism in your inner ears while you are boating, just in a slightly different way than when you are walking. You'll learn to respond to an impression of tipping in one direction by shifting your weight, or shifting your hips, just like you naturally do wiuth your feet when balancing on your toes, or stepping forward. You probably learned similar balance skills when you learned to ride a bicycle.

And practice paddling. You are more stable when you are going forward.

Best of luck

PGJ