Obviously advance planning would have been the solution to the issue with this dude, unfortunately this was my first example of a top heavy model, so everything was already in place.
The lead I bought was uniform in size, and slightly too big (I'm talking less than quarter of a millimetre too big, so it stuck out of the bottom of the base. The solution I used was to flatten it slightly, between a hammer and a metal mallet, and then glue it in place. It's not perfectly steady, but it's a lot better than it was and can even support itself on uneven terrain.
However, I did foresee this problem coming with my next model, my Chaos Marine Possessed Champion, and I worked to solve it before it became a problem. I worked the lead into the base decoration, underneath the rubble, and also on the actual underside of the base. The effect is that I know have a really tall and quite heavy model, but that's okay.
So, the lesson to be learned is that foresight is everything, but we all have to learn from somewhere.