Thanks, I'll try that. I just thought it was "Lots of influence" flowing into space. Guess I could have passed over occupying 7 or 8 planets 
Update - worked like a charm. Only curious if I would have had more points if I had finished in fewer turns.
p.s. re: help with part 3: my approach was to increase logistics as fast as possible: traded some (just paid $$ for it as soon as it was possible) and researched it - happily being boosted with research by the surveyor. And, to increase the effectiveness of the transports - docking at the start port lets you eject and boost the population to 6M each - so only one transport is needed for the first three planets.
And the idea I read from someone else - to take a large ship, new design, and just add transport mod plus as much engine as possible shortens the construction time and increase the moves per turn - immensely.
In short, as logistics went up I was able to combine more ships into Fleet 1 and probably could have completed part three without ever building a new combat ship.