A nice crossover exercise from forward fall to breakfall/freefall is koshinage as tori has very much control over aite and can prevent mishap quite easily.
*Provided* that tori actually knows what to do with that control and, ideally, is approximately the same size as aite. Breakfalling over the shoulder of someone taller than you is not something I'd recommend for beginners!
Which is a reason to recommend ukemi-focused classes and workshops. In most classes at most dojos, the focus is on the technique. But a vicious circle can develop: it's very difficult to learn how to do koshinage if your partner is afraid of the ukemi, but it's very difficult to develop confident ukemi if your partner is tentative about the throw.