There's a really neat thing about this, the relationship balances out at a certain orbital height, before it flips over so there's an orbit where your chronologically in synch with the ground.
That's only true with respect to a given locus of points on the ground, not the full surface. I.E., the relative velocity of the SV isn't the same for all points that may be measuring.
In practice the GR effect is compensated by the satellite at manufacturing, the SR effect is treated in the receiver - for just that reason.
In practice the GR effect is compensated by the satellite at manufacturing, the SR effect is treated in the receiver - for just that reason.