Background: I downloaded a copy of Balancer Reloaded from the Storm Over Civilization Forums, extracted it from the RAR using Stuffit Expander, installed it in Conquests Game Data/Conquests, then went to get it started in C3C. And had the same problem I had with Balancer as found under Play the World Game Data.
So I tried an idea I had, only to run into other problems having to do with missing files.
Since the previous solution had apparently worked, I tried it again where the new missing file was concerned, only (you guessed it) to learn that yet other files were not where poor old Tiger (G4 iMac, Leopard won't run on it) thought they should be. Finally I learned which files were missing (yes, it was tedious) and got them into place. Here now I present what I did
Now the Medieval Japanese file in question was supposed to be in a folder that didn't exist under Balancer Reloaded, so I simply got a copy of that folder from Sengoku/Art/Units, plus a copy of every other Folder that started with "Medieval Japanese" just to be sure. Then came the missing Balancer Reloaded/Art/Units/Nomad files. This is what ate up my time.
I did write down which files they were, where I found them, and where I put the copies. I even went and copied that write up to the clipboard, or so I thought. Only to learn that that copying didn't happen. So as best I can recall, here are the files I copied from Civilization 3 Game data/art/Units/Worker to Balancer Reloaded/Art/Units/Nomad
ScoutRunFoot2.wav
WorkForestLeaves.wav
WorkFortressHammer.wav
WorkIrrigatehoe1.wav
WorkJungleMachette1.wav
WorkMinePickAxe.wav
WorkPlantBag.wav
WorkPlantSeed.wav
WorkRoadShovelInwav
And lo did Balancer Reloaded load.
Give my advice a try and see how it works for you.