I suppose that the perfect score for the game, without any extra searching, would be as follows:
6 artifacts found x 10 = 60
6 artifacts activated x 5 = 30
6 artifacts connected x 5 = 30
12 perfect searches x 10 = 120
(assuming you got the artifact on search 1 and material on search 2, with no extra searches past that point.)
3 unused tools x 10 = 30
6 Hit point x 1 = 6
1 active utopia engine x 20 = 20
14 extra days x 5 = 70
(How did I calculate this? Assuming the 12 perfect searches above, you can cross off all skulls with the god's hand energy. Also, you will have found everything you need in only 8 days with no 'extra' searching [2 days in two locations since they have a double -1 bubble at the start, and 1 day for the other four locations]. That gives you the full 22 days minus the 8 you used for 14 extra days.)
Total = 366
Again, this is with no "extra" searching, as in the player STOPS searching an area the moment they have one material and the engine part. The above also assumes everything is done almost perfectly. I suppose you could attempt to make some complicated chart with extra perfect searches versus how many days you will spend and chart your highest possible score, but I'm content with the above. I only ever "extra" search if I have a free bubble and only to get another material for the crystal or so I can handle a connection screwup.
Actually, that brings me to a question. Activation can be restarted at any time, it says. What about connecting? Must you finish a connection when your start, or can you spend another material to start fresh?
Fun game. Not too long: the length gives me a great sense of achievment as I progress.
You can't stop a connection in progress or redo a connection you already made. If you make a bad connection, there's no way to make it better.
I've never calculated the perfect score before. I couldn't imagine getting consistently lucky perfect searches on every search. But your breakdown of the perfect game is cool to look at.