My understanding is that if you choose an F-key that doesn’t have a media function (such as F16) you don’t have to press fn.
Or you could check the “Use all F1, F2, etc. keys as standard function keys” option and then press fn to get to the media keys.
Another option would be to choose a non F-key for EagleFiler. For example, Control-Option-Command-E can be typed with one hand.