How about I add a new option (in addition to the current log(N) functionality) which would increase the age cost (X) by some fraction of the age cost (lets call this fraction Y) beginning at age Z and you get to set X, Y and Z?
So, for example, if you set the age cost to 1 and choose to increase it by 0.001 of the age cost per cycle beginning at 1000 cycles then you would have the behaviour you site.