• Why are my sources coming out in mirror positions on the sky?

This probably happens because you set up a simulation using the aips++ newsimulator package. Unfortunately the VLA and ASTRON people seem to have a few disagreements about fundamental parameters in aperture synthesis. The UVW coordinates (and therefore phases) calculated by MeqTrees and aips++ are 'back to front'. But MeqTrees does not store its calculated UVW coordinates in an aips++ Measurement Set; instead it relies on aips++ to do things 'right'. The way out of your dilemma is to do a Meq.Negate on UVWs calculated by MeqTrees. e.g.

# now define per-station stuff: XYZs and UVWs
for p in ANTENNAS:
  ns.xyz(p) << Meq.Composer(ns.x(p)<<0,ns.y(p)<<0,ns.z(p)<<0);
  ns.uvw(p) << Meq.Negate(Meq.UVW(radec=ns.radec0,xyz_0=ns.xyz0,xyz=ns.xyz(p)));

Oh, and MeqTrees and aips++ also disagree on the meaning of Stokes I as well, but that's another story.