Approximate Er of FR4 dielectric constant in mixed FR4 + Rogers board at 34-36GHz?

I have a mixed substrate design. Problematic part is wavegude to microstrip transition (ro4003) through FR4 substrate. While designing I've used value around Er=5 (FR4 for 35GHz). It seems to be underestimated. In reality prototype's central frequency probably pulled down by few GHz, because Er is much higher. By slowly tuning 35GHz source down by 200MHz constant improvement is observed. Simulation shows, that similar poor results may be obtained only if FR4 Er is 7 or even more. Is it a good guess?

Er of 7 sounds unrealistically high. Of course there's no specification for FR-4 at 35 GHz, but all published measurements for FR-4 qualities with improved high frequency behavior (there are some up to 10 or even 20 GHz) show flat, slightly decreasing Er.

Calculated Er of FR4 may go down vs frequency.
But the measured effective Er of FR4 decrease until certain frequency (somewhere between 1GHz and 3GHz, depending by moisture degree and temperature) and after that frequency, Er starts to increase.

https://www.sciencedirect.com/scienc...73043-main.pdf

IMO, at these wavelengths and dimensions you need to account for the non-homogeneous woven structure of FR4 laminates.

https://www.isola-group.com/wp-conte...ufacturing.pdf

Also, effective increase in current path length from metal surface roughness could be mis-interpreted as an increase in permittivity.

the Er at 30+ ghz is probably undefined. It DEFINITELY will depend on WHAT DIRECTION a line is going in...i.e. is will be anisotropic.