SE needs to tell everyone on BAL and GIL that the servers are going to be deleted in X (30? 60? 90?) days. All characters from those servers can transfer to A, B, C, D, or E and should click (link) to specify their preferred server by X date. As compensation for the inconvenience, A, B, C and D rewards are being offered to players who actively participate in the server rebalancing program. All characters that have not been assigned a realm by their player before X (date) will be moved to a new server via random selection.

By giving ample time, SE would allow communities (RP, LGBTQ, Raiders, etc.) to decide where they want to go. By offering rewards that are obtained by actively being a participant in solving this problem, they could reduce backlash and make the transfer process less frightening and more productive.

This is probably not going to be a popular solution, but in theory it would end the problem.