Actually, there are two things to investigate here:
1) why does the client balancing not work
2) why do most of the clients choose only one AP
1) Can the APs talk to each other on the LAN side? That is needed for distributing the client information from AP to AP. Then there are a couple of event logs for "load balancing" decisions. Do they show up, do you see load balancing decisions?
2) Did you do a validation survey to verify that you have different "best" APs in different parts of the room? Here it really could be that antenna-positioning is not optimal. Have you checked if the transmit-power of the APs are low enough?