What if there was a gamemode using Attack/Defend maps, preferably with 5 control points. However the maps only have far-end control points or at least the center control point. Depends which is fairer. Incidentally Hide and Seek or simply large elaborate maps would also be practical.

Each player has Knuckles emerald radar which helps the individual player seek out an emerald shard which is randomly spawn somewhere on the map in a hidden, non-obvious but still accessable location. Either all three emeralds are hidden which may make the game go quicker or the emeralds show up one at a time after every capture. Maybe there can be some algorthim of emerald spawning to make sure the emeralds are hidden fairly and not too close to a specific side to be unfair.

Normally in SA2Bs competitive mode the emerald is secured when collected and those with at least 2 shards automatically win. For TF2 we can do it a bit different:
When a player finds an emerald shard, that shard will behave like a Special Delivery briefcase. The player has to take the emerald shard to either the capture point in the center or the capture point closest to their home base. Enemy team can attack and take that shard from them just like usual intel briefcases and when dropped the emerald shard will dissapear and rehide itself after 20-45 seconds or so.

The team that secures all three pieces of the master emerald wins.