"From our inertial frame, the ground below us is moving toward us" makes a lot of sense to me, but doesn't seem to be quite the same as "the surface is accelerating up at you relative to the gravitational field". The former is with respect to the inertial frame of the faller(s), the latter seemingly with respect to the inertial frame of some shared gravitational field.
That said, your description does kind of explain it for me, unless I am misunderstanding, though at the moment I only get it as a "negative" argument: we are being accelerated upwards/outwards with respect to the field's reference frame, because otherwise we would be moving along our natural inertial path.
It is still a bit puzzling that if the ground disappears we appear to accelerate, whereas my current reading of what you wrote seems to imply that we would immediately return to our "inertial path".
What I'm really wondering is if all of this "acceleration relative to the field" business is a misleading abstraction, and "relative reference frames" fix it (and indeed that was my very primitive understanding of relativity). However, on balance it seems much more likely that I'm simply misunderstanding things.