I have also thought that straight up would be the best course of action.
First, they cannot fly straight up, so they certainly can't chase the drone except from above. Second, their natural prey never attempts to escape by going straight up, so I would think that it would catch them completely off guard.
That being said, an eagle will probably be diving down from above. If the operator can actually see the attack coming,
"up, up, and away" might be a bit better. Particularly if the operator can impart an unpredictable path. A multitude of directional changes while rising will really screw up their attack. Given that so many of us cannot actually see the drone while we are flying it, despite government rules to the contrary, the chance of escaping an eagle attack are probably pretty low.
I watched with amazement as an eagle flew several thousand feet above the peaks of the mountains in Glacier National park. Probably these mountains:
It was a tiny dot that I could barely see flying far above a 9300ft peak with my binoculars. If a bird can navigate at that altitude, even when using thermals, it is extremely unlikely that a drone can hope to escape from them when limited to 400 ft off the ground.