My puller slipped off as well. I usually use a set of very good pullers I borrow from Canadian Tire (they lend specialized auto tools) for such jobs, but I tried my own 'generic' puller and had to improvise.
1) Even without the tit, you may be able to get more puller hooked on. I ground the ends of my puller down (originally for thrust arms) in order to make em 'grabbier'.
2)I know exactly what you mean by tilting and slipping off. If your using one of those two or three arm generic pullers, then the arms are able to spread outward and slip off. I use a 6 or 8" C- clamp to hold the arms on, then popped it off.
If this doesn't work, get a better puller (there are many different shapes which will work better than the generic). Or, maybe someone here has another non-puller method.
Dave