>>26849424A phone recording can work fine. Plenty of people have done it before, like at Anime Boston. Some phones have apps that make it possible to record audio in the background while also letting you use other parts of your phone, like posting messages if you want to do that during the panel itself. If you don't want to use your phone, you can also get something like a secret recording device.
Pic related is an example of what is available. Forty dollars, small necklace, capable of recording conversations for a full day. Can't speak to quality, but I imagine something like this could pick up the amplified voices of a panel.