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You're in good company. So did Isaac Newton...

I would think that measurements of earth's acceleration toward the sun that show a direction that is 8.3 minutes ahead of the apparent position of the sun in the sky also demonstrate a propagation speed that is virtually (at these distances) instantaneous. That is, the earth is not accelerating toward where "gravity waves" are supposedly reaching the earth together with the photons that left the sun 8.3 minutes previously but toward where the sun actually is.

You are confusing instantaneous with continuous.

The effect of Gravity as a field is based on a continuous "warping" of space based on the presence of mass. And mass such as the sun does not instantaneously dissappear, as in the thought experiment cited of a vanishing sun. Every "now" is based on the influence of where everything elsewhere "was" at this moment's light-horizon...

If the sun exploded from its center in an emmense explosion such that all the remaining mass of the sun was accelerated into a spherical shell expanding at near light speed from the center of the sun, once this shell of matter passed the earth, what was left of the earth would proceed in an essentially straight line - no longer an orbit - based on the long-recognized zeroing out of the gravitational attraction of matter outside a sphere, modified by the reaction of the collision of the expanding debris impacting the earth, and physically propelling it in a slightly different direction...

I would think that measurements of earth's acceleration toward the sun that show a direction that is 8.3 minutes ahead of the apparent position of the sun in the sky also demonstrate a propagation speed that is virtually (at these distances) instantaneous. That is, the earth is not accelerating toward where "gravity waves" are supposedly reaching the earth together with the photons that left the sun 8.3 minutes previously but toward where the sun actually is.

But where the "sun actually is" doesn't really move that much, relative to the Earth. Don't let the apparent "movement" of the sun across the sky as the Earth rotates fool you.

The Sun pretty much sits in the same spot (i.e., right in the middle of the solar system), so there's no testable difference between the effect its gravity has on our orbit if "instantaneous", versus the effect it would have 8.3 minutes delayed.

If the Sun actually *were* circling the Earth in the way it *appears* to, then yeah, an 8.3 minute difference in gravity would be measurable. But then, it would also be circling us at over two million miles per hour (3% of the speed of light)...