The problem is that your return to Earth would slowly move you back down the dilation losing the gains.
You can take two routes to a restaurant. One is very short but curvy and has a slow speed limit. The other is a really long straight shot with high speed. You can think of your scenario as such a case where even though the straight path is longer, it takes the same “time” to get to the restaurant.
You would be taking the faster, longer route while Earth takes the windy slow route but as you arrived back you would still be in sync.
Edit to add: Spacetime is a single thing which is why the above behavior the case.
The problem is that your return to Earth would slowly move you back down the dilation losing the gains.
You can take two routes to a restaurant. One is very short but curvy and has a slow speed limit. The other is a really long straight shot with high speed. You can think of your scenario as such a case where even though the straight path is longer, it takes the same “time” to get to the restaurant.
You would be taking the faster, longer route while Earth takes the windy slow route but as you arrived back you would still be in sync.
Edit to add: Spacetime is a single thing which is why the above behavior the case.