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Everything I've been patiently explaining is still true; the bigger a thing gets the more squishy it is and the more it absorbs energy internally rather than rebounding elastically. Conservation of momentum is easily observed for small, elastic-rebounding things but it has trouble in high-friction environments. (It's actually still holding, but the momentum changes are disguised as heat within macro objects.) The Earth is very squishy. Especially its clouds and oceans.

But I'm going to try a whole other viewpoint, since it seems you've got that one barricaded and nothing is getting through. You concede that the push must be very, very, very, very tiny. It is that. (For reasons I've beaten to death I suspect it is close to zero. Note that a billion times zero is still zero.)

At any rate it is below noise level.

There is a noise level. The Earth is struck daily by space objects of non-trivial mass and momentum. The tiniest imbalance in that bombardment utterly swamps your trivial, utterly unmeasurable solar sail effect. Then there's the gravitational pull of near-neighbors the Moon, Venus, and Mars.

You can't have a cumulative effect from a "signal" that's dwarfed by the noise. It doesn't accumulate. It never goes anywhere.

Lest I forget: yes, the Earth is still at one AU from the sun. But if it ever does move out to the orbit of Mars the solar pressure won't be so much. You pushed it out to 20 gazillion something-or-others with no decrease in solar photons. That's another way your answer is wrong. Not that it matters.