As Lyx said, you don't have to start a new game. It takes effect immediately.
Taimat, Modifying morale per troop requires an extra line. I went ahead and added a divide to the equation, so if you want to modify the number of troops per morale lost you will need this script:
get_player_party_morale_values -1
50 1650 2 1224979098644774912 648518346341351424 2133 2 1224979098644774913 0 6 3 1224979098644774914 0 1224979098644774912 1652 3 1224979098644774915 648518346341351424 1224979098644774914 4 0 1507 1 1224979098644774915 2105 2 1224979098644774913 3 5 0 1653 3 1224979098644774916 648518346341351424 1224979098644774914 2108 2 1224979098644774916 1 2105 2 1224979098644774913 1224979098644774916 3 0 3 0 2133 2 144115188075856282 1224979098644774913 2170 3 1224979098644774917 1369094286720630785 360287970189639680 2122 3 144115188075856283 1224979098644774917 7 2133 2 1224979098644774918 144115188075856283 2106 2 1224979098644774918 144115188075856282 2105 2 1224979098644774918 50 2133 2 1224979098644774919 0 2133 2 144115188075856284 0 6 3 1224979098644774920 288230376151711778 288230376151711792 150 1 1224979098644774920 4 0 33 3 1224979098644774920 288230376151711778 288230376151711790 2105 2 1224979098644774919 1 3 0 527 3 1224979098644774921 1224979098644774920 1 2105 2 144115188075856284 1224979098644774921 3 0 2105 2 1224979098644774918 144115188075856284 4 0 31 2 1224979098644774919 0 2133 2 144115188075856285 30 2106 2 1224979098644774918 144115188075856285 5 0 2133 2 144115188075856285 0 3 0 2133 2 144115188075856286 0 4 0 32 2 144115188075856027 0 1 1 936748722493063280 2133 2 1224979098644774922 72057594037927936 2122 3 144115188075856286 144115188075856027 10 2108 2 144115188075856286 1224979098644774922 2112 3 144115188075856286 1 31 2106 2 1224979098644774918 144115188075856286 3 0 2112 3 1224979098644774918 0 100 2133 2 72057594037927936 1224979098644774918
The bits I added are in red. The 50 is just the code telling it how many lines of script it is supposed to be reading, it was changed from 49 to 50 so it will read the extra line correctly. All the other highlighted red parts is the divide coding, with the blue number following it being the number of troops per 1 morale penalty. Keep it at 1 for no change, or whatever number you want to require higher troop numbers per morale penalty. A 5 would mean every 5 troops minuses 1 morale.
I also highlighted the two numbers from the first post (morale penalty per hero, and morale bonus per leadership) in lime green just in case you were having trouble finding them with the extra line of coding.
Enjoy. I didn't really think about it before, but simply cutting the morale per regular troop in half allows for larger armies without the problems that way more morale per leadership can cause. Like the no food penalty of 30 being pointless since leadership was adding so much

Oh, and TJL: the default max troops is 10 base, 3 per leadership, and 1 more per 25 renown. As shown in the companion limit script in the topic.
-edit - for those of you looking at this for 1.003, the script has changed but this change can still work. The first number has changed to 44, since 5 lines of code were removed in 1.003. So that needs to be 45 if you add in the line. Other than that the code doesn't need to be changed, if you put it in the right spot it still works.
It does have one minor oddity - it only stores whole numbers, so any odd numbered troop stacks will be halved and rounded down - in effect giving a free troop for morale calculations for every odd troop stack. In one stack of troops it would only amount to .5 morale, but if you had 10 stacks, all odd, it would be 5.