Second suggestion :
monitoring deal with stations
Maybe could we pay stations, to let them send us data from their system and neighbouring systems from a number of turns.
Or they could also send a probe (see previous suggestion) for a given price.
This opens the door for
different station types (on top of the different strength there already are) :
Some would monitor their system only, some could monitor neighbouring systems too.
Some would be able to send probes, some wouldn't.
The could also be a maximum amount of damages that a station can repair per turn (or until you leave the system and come back).
Back to the probes, I imagine other possibilities when the probe halts :
Getting help : if there is a friendly ship in the system the probe halts, then a dialog would open and the ship would propose its help. If we accept, then it starts moving, one system per turn toward us. Then the probe stays there and keeps monitoring the system.
monitoring/probing deal : if the probe halts in a system with a starbase, then a dialog opens proposing to start a monitoring deal with the station (or send another probe, if there is the option). Then the probe stays there and keeps monitoring the system.