Best way to suspend beam end from cable
I'd do a hybrid of your other ideas: Drill through the beam as you would for an eye bolt, but simply feed the cable through and terminate it with a stop of some sort. You could loop back on itself and use a clamp. Back it with a washer to prevent pull-through of any sort. 

I did almost exactly this with a circular (ring-shaped) suspended treehouse in a huge white pine at my old place. It held solid for years.