The flexcompute python code does a very good job in simulation for controlling the undesirable modes, and we can see relationships between the parameters they use, it however does not evaluate the impedance after adding the vias.
Altair also gives a decent general guideline for vias, but they too do not describe the impact vias have on impedance.
https://help.altair.com/feko/topics/feko/user_guide/appendix/how_tos/feed_cpw/construct_cpw_feko_t.htmI did read elsewhere that the spread distance should be near 1/2 lambda (1/4 wave to left of center signal track, and 1/4 wave to right of center signal track). This after doing std GCPW design.
In some other online discussions a user found discrepancy of 4ohms due to vias because they introduce some reactance.
If it's not a tool that enumerates optimal values for the GCPW design, then perhaps a tool where we can input values manually and the tool calculates impedance account for the reactance from vias.
All that said, in std GCPW the signal plane side ground fills need to be connected to the ground plane side, so it needs vias somewhere, or the ports(in out ports) need to attach it's ground to all the ground fills. I assume adding via fencing enhances this setup, yet the via reactance needs to be accounted for.
Using just some general rules (as defined by many online sources), for fencing, distance from trace edge should be 2-3x the pour gap "S". Via spacing around 1/8 to 1/10 lambda of highest frequency in application.
So design std GCPW, take the side pour gap and x2.5 that as value "d", then center of via shall be placed "d" away from the edge of the signal trace. That's good, but the vias still impact the impedance derived from std GCPW design, which is what I am trying to obtain, so that something like pour gap or trace width can be adjusted to account for the vias.