Unfortunately, this didn't work for me. I also deleted the mods folder again and reapplied it after the changes to see if it worked and it didn't work either.
I chose a random starter and fought Cain and the TypeBattleIcons mod is working for me so I can confirm that the mods are loaded.
I created a 3rd save file and chose a starter and it still isn't giving the option to change my starter.