I am using several power strips and all receptacles in the train room are GFCI. I have no problems. There is no circuitry in any power strip or GFCI the in any way inhibits anything in the GROUND signal path. The Grounded conductor and Hot conductor do go through some filters and surge devices in power strips. There are no surge devices or filters in Ground Fault devices either breakers or outlets.
You description of the problem also is not clear. Ground wire to what? FRom where ?
Do not ground the tracks, anywhere.
The ground on the signal booster is the ground of the AC line on the power plug. The round longer pin on the plug not the 2 parallel power conductors.
With the Signal booster unplugged use an ohm meter to check for a ground or low resistance between the outside rails of the track and the AC power ground. This should read an infinite resistance or at least very high resistance. A low resistance means that the outside rails are grounded somehow. This must be fixed. Start disconnecting everything from the track until the ground goes away. The railroad should not be grounded ANYWHERE.
I ran alot of hardware cloth ( 1/4 inch mesh screen type wire ) under all of my layout tracks on all levels as I was building the layout. All of that is grounded to the electrical system ground. That got me most of the way there but I still had problems. That is when I designed and built the first TMCC booster which was Vacuum Tube based. That solved all my problems.
The signal booster places a signal between ground ( the electrical system ground ) and the outside rails. If the outside rails are grounded then you have esentially shorted the output of the signal booster and it cannot work.
Jim
LeFevre Engineering
James L. LeFevre P.E.