> if you choose the right reference frame, it would seem that the return trip requires the twin to experience negative acceleration.

While in relativity velocity is relative, accelerations are not. Accelerations can be measured and felt. Easiest example. You're driving along a perfectly flat road in the back of a windowless truck. There is no experiment you could do to determine what speed you're going. All speed feel the same. But if the truck accelerated- sped up, slowed down or even turned, you would notice.