I wouldn't pot them deeper than they are currently growing. You could behead and root the Aeonium to keep it from being so top heavy, or put the whole pot in a larger clay pot to stabilize it.

Keeping the stem underground could encourage it to rot.

If it were my plants, I would definitely pot deeper. I have done it many times without rot occuring. If you think about it, a cutting has stem planted underground, so what could a few more inches planted underground negatively cause? Besides, you would keep the size of your plant because you wouldnt have to bury the new rosette's stem several inches underground.

I had a problem like this, and what I did was plant it at normal level then pile stones ontop of the soil around the base of the plant to stabilise it while it built a better root system. Then I removed some of them after a few months :) the only issue with this was the soil stayed damper longer

That was a good idea, Rachael. I did pot mine down a bit, but I agree that it should stabilize when roots grow in the soil. It was potted in what was basically a tall cup when I bought it.