The floating feed point issue almost always comes down to how the simulation anchors the reference plane at the port location. When you put a coax feed right on the edge, the solver needs a definitive ground plane defined immediatly adjacent to that connection point to properly calculate the impedance and S-parameters. Simply tying the shield to a net named ground might be enough for DC analysis, but EMerge needs that spatial relationship defined in the geometry and the port setup. Try adding a small, dedicated ground pad right next to the coax transition, and then assign that pad specifically as the reference for the port definition itself, separate from the global board ground net. This forces the solver to treat that transition as having a known reference. For the phase-shifter states, you cannot just run them one after the other thru the GUI if you want a full matrix of results. EMerge handles parameter sweeping via the configuration script. You need to define the variable you are changing, like the tuning voltage or phase shift angle, as a parameter in the input file. Then, you use a loop structure within the solver settings to iterate over a list of values for that parameter. For instance, you define a list of angles from 0 to 360 degrees, and the solver will run the analysis for every step in that defined range.
It is critical to check the solver input file configuration for the 'parameter sweep' or 'multi-state' section. If that isn't set up correctly, it will treat the shift states as individual components rather than variables in a sweeping analysis. It should be configured as a sweep over a defined range of values, not just a list of static settings. This method of sweeping parameters is standard for all the FEM solvers because it allows the solver to calculate the resulting impedance and phase response across the entire operational range in one pass, which is much more efficient than running a dozen separate simulations.