Hi,
If you decrease the cross sectional area of the core then you have to increase the number of turns. For small changes (which is probably all you should allow anyway) less than about 40 percent, it comes out to increasing the number of turns by half the decrease in area. For example, if the area decreased by 10 percent, then you should add 5 percent more turns. So if you had 100 turns to start with, this would mean you would need 105 turns as an approximation, and that should be close enough considering other variables which we have no control over. For a ratio of 0.68 to 0.5, which is 36 percent, would require 18 percent more turns, so if you had 20 turns to start that would mean adding 3 to 4 more turns. The DC resistance will be roughly 20 percent higher so the Q comes down a bit, which only means the selectivity will suffer somewhat if it is used as a tuned circuit. If it is used as a DC rf filter it will just decrease efficiency.
Yeah if you use an inductor in series with some resistive load and the signal at a particular frequency gets attenuated more than with a different inductor (bead on wire) then the first inductor is bigger than the second.