The mission log has saved my progress. All objectives are check marked except for destroying active probes. The destroy damaged probes is check marked but shows 0/4 destroyed. Any probes I destroy do not count to mission objectives.
I don't know which aspects of this are significant but it worked for me and has done for some others. In the Damaged Drones area tilt your ship up and engage full speed 'til you're prompted something along the lines of nothing on sensors and it offers to change instances. Accept the switch, and I ended up in the correct area for Active Drones. Now completed that and subsequent missions and I'm watching the load screen for the Sol System as I type.