I agree with Sugs that a global chat moderated by 2 (or a few) admins is definitely not enough, and will certainly lead to over-restricive decisions. Giving a limited power (e.g. preventing a user to post in the global chat for 1 hour) to a lot of "trusted" users (long-time and/or number of games played) seems a good option to me. You could limit the risk of power abuse by requiring several trusted users to ask for moderation.
Example: a tiny icon (cross or red thumb or face with duct tape on the mouth) could be displayed next to all user names in the global chat. In case of rude language or spamming, any "trusted" user could click on this icon to ask for moderation. If a certain number (20? 100? depends on what is required to be a trusted user, I believe) of users ask for moderation, the moderation is triggered immediatly (no global chat for this user for 1 or 2 hours, or more). Then, when they have time, the admins (and maybe a few chosen moderators) can review the chat messages of a moderated user to see if they want to ban (or something else) this player.
The "shut up" icons in the global chat could be displayed only for "trusted" users.
And if you see some cases of power abuse from trusted users when reviewing messages, you could remove them from trusted users.