There's nothing they can do.

Their servers just can't handle this many people. It's not a bug or code that can simply be quickly edited and changed with a quick maintenance. They would have to upgrade their server infrastructure...again... or somehow put together a built in queue system for solo instances so people don't feel the need to spam NPC's, but even that won't help the actual strain on instances in general causing mass disconnects in duties across the board.

When they put out a statement earlier saying they were sorry and to please be patient and wait, it's because that's literally the only thing that can be done. Wait for the wave to subside and relieve stress.