External to internal antenna setup doesn't increase signal power
The large antenna is collecting a portion of the cell tower's energy which falls within its "antenna aperture". Your system is then radiating this energy from the small antenna in all directions.

(Not really, of course, but you see the point).

Only a small amount of this power is being re-radiated in the direction of the cell phone's antenna.

I expect you could detect the improvement in signal strength if your chamber had a higher level of attenuation. But as it is it's getting swamped out by the direct signal which is coming from the cell tower.