QUESTION:
Why not send up a "re-transmitter," or some sort of satellite to
relay a strong signal from Galileo back to the ground?

ANSWER from FAQ:
The project briefly studied this option, but quickly determined that,
given the short amount of time in which the relay satellite would
need to be designed and launched, a relay would be prohibitively
expensive.

There were also significant unresolved technical problems related to
both orbital mechanics and telemetry. Engineers first proposed
having a relay satellite that would follow Galileo closely, like a
well-trained dog. But, the amount of propellant needed made the
mission too expensive. Even keeping the relay satellite within a few
million kilometers of the spacecraft throughout the entire two-year
orbital tour would be a difficult (if not impossible) engineering
problem, given the limited amount of fuel on board a relay satellite.
Finally, the relay antenna itself would need to be comparable in size
to Galileo's original high gain antenna, which would add to the
expense and complexity of a relay mission.