Walk around to the opposite side of the gyro wheel. If the acceleration is due to the rotation of the gyroscope, it still points out radially. If it was due to a mass out beyond the rim, you're falling on your head.
General Relativity may seem counterintuitive, but experimentally it really does seem to be the way our universe works. Starting out from the position that absolute motion is meaningless has proven remarkably fruitful. It's also something a lot of very smart people have been thinking about for a hundred years. Whether or not you find Mach's arguments plausible, they're fundamental philosphical claims and can't simply be dismissed through a half-baked thought experiment.
In that case, it wouldn't be drawing you outward no matter where you were located. So, spinning would be "you feel a gravitational force", and a ring of mass would be "you don't feel a gravitational force".