You've got the math wrong for the scythe. You're doing *2 rather than *4.
I feel like trying some more realistic math.
Let's say a 10th level barbarian (+1 keen weapon, belt of strength +4). 26 strength when raging (16 base, 2 levels, 4 item, 4 rage). Power attack for 5, because more will result in hitting on only a 3+ or something.
3.0 stacking
Greatsword (15/x2) = (((7+12+10+1)*13)+(((7+12+10+1)*2*6))/20 = 37.5 average damage
Scimitar (12/x2) = (((3.5+12+10+1)*10)+(((3.5+12+10+1)*2*9))/20 = 37.1 average damage
Scythe (18/x4) = (((7+12+10+1)*16)+((7+12+10+1)*4*3))/20 = 42 average damage
3.5 stacking, replace keen with another +1
Greatsword (17/x2) = (((7+12+10+2)*15+((7+12+10+2)*2*4))/20 = 35.65 average damage
Scimitar (15/x2) = (((3.5+12+10+2)*13+((3.5+12+10+2)*2*6))/20 = 34.375 average damage
Scythe (19/x4) = (((7+12+10+2)*17+((7+12+10+2)*4*2))/20 = 38.75 average damage
20th level orc barbarian with 46 strength, +5 weapon, power attack for +40 damage:
3.0 averages, in order - 98.75, 105.7, 110.6
3.5 averages, in order - 90.85, 94.375, 98.75