For line between Feig module and BNC connector:

Coplanar Waweguide
Formula from p. 67 in

Antennas
from Theory to Practice
Yi Huang
Kevin Boyle
J.Wiley
ISBN 978-0-470-51028-5 (HB)

dimensions in mm
er = 4.43;
d = 1.5;  # board thickness
G=0.20; # pcb's Keepaway
W=1.5;  # pcb's Thickness
k= W / (W+2*G);
kp = sqrt(1-k*k);
ere= ((er+1)/2)*tanh(0.775 * log(d/G) + 1.75) + (k*G/d)*(0.04 - 0.7*k + 0.01 * (1-0.1*er)*(0.25 + k));
Z0 = (30* pi / sqrt(ere)) * (1/pi) * log(2 * (1+sqrt(kp))/(1-sqrt(kp)))

W=1.0
Z0 =  57.202

W=1.5
Z0 =  51.587

But then, it don't include effects due to the ground plane
my impression is that the ground plane would lessen Z0

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Vias can be done with dia.0.6mm wire instead of through hole plating.