I thought about that problem... but for several Huts. The length of time to get all is extended not shortened if each hut is upgraded as soon as possible. The reason is the Hut stops making the archdruid as soon as it becomes level ten. Only level nine makes the archdruid upgrade.
So saving them at level 9 until all are able to be upgraded will get it all done faster.
This is true, however it makes no difference in the long run. Simple example of 2 huts without the archdruid upgrade (no blue galaxy ; but it doesn't change the comparison, just speeds up all cases).
1) Wait for both: 150 days and you have them both.
2) Finish one asap, and then the other. 75 days, 1 is up. +150 additional days to finish the 2nd.
So over the 225 day comparison period:
Option 1 has 2*150 = 300 l9 collections, and 2*75 = 150 arch collections.
Option 2 has 2*75 + 1 * 150 = 300 l9 collections, and 1*150 = 150 arch collections.
So it's just a matter of which one appeals to you more