Jordan -- Welcome to the Puritan Board!
I hope that your first post/thread doesn't generate too many fireworks for you.
I rejoice to hear that you have embraced EP and also that you are not running for the exit door of your church. Unity with the brethen, and honoring the authority that is over you, and endeavoring to live at peace with those around you inasmuch as possible, are all vital components of the Christian walk. I would submit that
not singing hymns in public worship is no disrespect to those around you or over you, and to do otherwise is to compromise the principle that you embrace. You are serving God, not man, by refraining from singing the hymn, and as you do so, you must find that balance between honoring Him and those around/over you.
I say this as one who has "served time" in non-EP churches, although I am blessed to be part of an EP denomination at present.
Respectful silence, reading along in your Psalter (can you find out what hymns are being sung in advance and do some advance homework to find a corresponding psalm?) or Bible, praying...these are all reasonable ways to redeem the time while the congregation is singing a hymn.