You don't need myth gear to do coil. If you've got full darklight with a relic weapon then you should be able to fill any coil slot for your FC. If you want to go the extra mile, primal weapons, primal accessories and/or pentamelded crafted accessories are even better options that don't have cooldowns or are very short (primal wep).

Once you fill that slot, *then* you should start gearing that class with myth and/or CT gear. This way your limited drops aren't wasted.

If you take a slot, and then they replace you or want you to switch classes after you've already spent the myth/CT drops for it, that sounds like a problem between you and the FC.