We present an improved model for the antenna phase center motion effect for high-gain mechanically steerable ground-based and spacecraft-mounted antennas that takes into account non-perfect antenna pointing. Using tracking data of the RadioAstron spacecraft we show that our model can result in a correction of the computed value of the effect of up to 2×10^-14 in terms of the fractional frequency shift, which is significant for high-accuracy spacecraft tracking experiments. The total fractional frequency shift due to the phase center motion effect can exceed 1×10^-11 both for the ground and space antennas depending on the spacecraft orbit and antenna parameters. We also analyze the error in the computed value of the effect and find that it can be as large as 4×10^-14 due to uncertainties in the spacecraft antenna axis position, ground antenna axis offset and misalignment, and others. Finally, we present a way to reduce both the ground and space antenna phase center motion effects by several orders of magnitude, e.g. for RadioAstron to below 1×10^-16, by tracking the spacecraft simultaneously in the one-way downlink and two-way phase-locked loop modes, i.e. using the Gravity Probe A configuration of the communications links.