I might be a little dense to this subject, but I would like to ask a question relating to this one

( Is gravitational time dilation different from other forms of time dilation? )

but asking if this can be extended from gravitational time dilation to acceleration-induced time dilation; that the time dilation under differing acceleration (between gravitation and propulsion) are not symmetric as they are in inertial frames under special relativity

The heart of what I want to know;

If a spaceship is accelerating Toward the center of the Earth at an acceleration greater than earth's gravitational "acceleration", does the spaceship (ignoring or correcting for doppler distortion) percieve clocks on earth to run fast in from their reference frame?

It seems to me that they should; the spaceship's acceleration should give rise to more-distorted spacetime than Earth's gravitation, no? By equivalence, would this be akin to observers watching the flow of time deeper in a gravitational well than the are?

I might be a little dense to this subject, but I would like to ask a question relating to this one

( Is gravitational time dilation different from other forms of time dilation? )

but asking if this can be extended from gravitational time dilation to acceleration-induced time dilation; that the time dilation under differing acceleration (between gravitation and propulsion) are not symmetric as they are in inertial frames under special relativity

The heart of what I want to know;

If a spaceship is accelerating Toward the center of the Earth at an acceleration greater than earth's gravitational "acceleration", does the spaceship (ignoring or correcting for doppler distortion) percieve clocks on earth to run fast in from their reference frame?

It seems to me that they should; the spaceship's acceleration should give rise to more-distorted spacetime than Earth's gravitation, no? By equivalence, would this be akin to observers watching the flow of time deeper in a gravitational well than the are?