OK , now that the superglue idea is thoroughly explred (and forgotten I hope!!
) Lets discuss reality.
In addition to what John said , try to remmeber that even when drifting , its nice to keep the eel pointing at you. as long as you are pulling , even a little , on the head to keep it pointing towards you , they won't get tangles. So when drifting , you got to let the line out at a rate that lets the eel move out but still keeps it pointing towards you. Just opening the bail and letting it tumble along freely will get you all balled up. You can still let it ride the current and keep it under control if you practice . Always feel it pulling on the line.
Try going to a beach with no current and casting out. Using an Ambassaduer 6500 reel , you should retrieve the eel at a rate that takes about ten seconds for one turn of the handle. That;s very slow and that's what you want. get a feel for how much pull that puts on the eel. now when in the current , let line out so you maintain about the same amount of pull that you did when slowly retieving on the beach at the rate I described.
In addition to keeping the eel untangled , you'll also be in touch with it better for when you get a hit.