Phoenix Dawn works same in normal dungeons and deep dungeons. Just needs to be out of combat.

What would be nice is having another source of them and maybe allow for stacking up to 3.

If tank holds you hostage you are 100% justified to report them, but do communicate with them before. Sometimes a gm will get them out even before the duty ends (seen that happen when a tank was trying to solo last boss of DT alliance raid from 10%)