I think you're trying to pump too much bandwidth through that poor little 16 port. I would recommend upgrading, or trying to distribute the load on that to an additional switch. Also, I would recommend going through your house with WiFi analyzer, and adjusting the channels the Access Points you have broadcasting so that there is minimal interference. I don't think DHCP is your issue, but it's worth a shot.
For DHCP, you could decrease the lease time significantly (to 12 hours maybe?) instead of manually assigning addresses.
