I think that the number of turns are integrated into the scoring formulae as a divisor of the accumulated score, and functions as an increasingly depreciation of every turns score as long as additional turns are added.
Perhaps in a way like
(SumOfScoreTurn1/Nt) + (SumOfScoreTurn2/Nt) etc = TotalScore
Nt being the number of turns that have been played.
A Turn1Score of 100 would deliver 100 points to the TotalScore if the game is ended on Turn1. If ended on Turn2 it would deliver 50 points, or only 10 points on Turn10.
However as long as this depreciation could be overcome by the collection of additional score each turn the TotalScore will rise, although this becomes increasingly difficult the more turns are added. As a rule of thumb as long as you can still maximize one or more of the different increments that attribute to the sum of each turns score (population, military ships etc) the score should also rise.