Any way to address a player's character besides the following methods?

Getting the Player

It doesn't really matter how you define the player. In a LocalScript, LocalPlayer is the best method. There's so reason to use anything else to define the Local Player in a LocalScript. In a regular script, you can get Player's from the PlayerAdded event, or if you somehow get the character of a Player you can use GetPlayerFromCharacter.

There are tons of ways to get the Player in a LocalScript, but it's best to use LocalPlayer, so there's no use in telling you other methods.

Getting the Character

If you already have the player, getting the character is as simple as player.Character. If you're using a touched event, there are always methods for getting the Character, and checking for a Character.

Good Luck!