I am a little confused because an object with velocity would experience smaller elapsed time compared to an object that is not. But in GR elapsed (proper) time is maximized by free fall who have velocity right?
An inertial frame $A$ calculates that the clocks in another one $B$, with a relative velocity $v$ tick slowly. (A person in $B$ is aging slowly for them). And that is symmetrical. The frame $B$ also see $A$ aging slowly.
In an accelerated frame $aF$, a free fall frame that is momentarily at the same speed of $aF$ will calculate the clocks in $aF$ ticking slowly. And that is not symmetrical. The same for a gravitational field.
But that conclusion can not be automatically extended to an arbitrary relative velocity. If a someone jumps from an acelerated rocket for example, after some time will reach relativistic velocities (as measured by the rocket crew). The crew will then calculate the free fall clock ticking slowly than theirs.