The heat pump itself probably doesn't need 60A - there should be a data plate on it. It's probably more like 20-30A, and maybe even 15A (but at 10-years, the efficiency it probably wants something like the 20A). The air handler is primarily just a fan with the exception of the heating elements. It might be powering some from the 'internal', standard wiring, and the 'extra' heating elements are off the second breaker. So, of the three breakers, the only one that can probably be downsized is the one for the heat pump itself. The only way to know is to open them up and look at the data plates, and, since you don't need to install all of the possible heating elements in the air handler, see what's there, and then determine if it will still be okay if you downsize a breaker. I doubt you'd be able to eliminate one, and downsizing doesn't help you if you need more panel space.
I don't think code would allow you to tap off that feed, but I'm not sure.
Best to run a new circuit.