Dungeons - Trash] For trash DPS AOE has gotten really strong to the point it can be tough to maintain threat if you mess around too much in Deliverance, especially against Red Mages. I try to keep ~50 Beast Gauge available at the end of each pull so I can open pulls with Steel Cyclone rather than Overpower, which is typically enough to establish threat indefinitely (and is easier to target when running through enemies). I find healers are able to contribute more reliable AOE DPS against trash when I'm in tank stance and using Equilibrium + Cooldowns -- I can go Deliverance to use Decimate every few GCDs, but the extra incoming damage means the healer needs to be 100% focused on keeping me up and can't contribute as much to DPS. So I don't think Stance Dancing is something you really need to worry about on trash pulls unless if your healer is dpsing their heart out and still looks bored.
[Dungeons - Bosses] I try to enter boss fights with 100 Beast Gauge if possible. Start in Defiance, run in, Tomahawk, and weave in Onslaught for a huge and instant burst of enmity. That'll put you at 80 Beast Gauge -- do one Storm's Eye combo to get your damage buff (and 100 Gauge), then swap stance to Deliverance. Heavy Swing, weave Berserk/Inner Beast, Fell Cleave, Fell Cleave, Infuriate, Fell Cleave, Maim, Fell Cleave, Storm's Path, Fell Cleave, Fell Cleave. Depending on Skill Speed you might be able to fit in the magical 7th Fell Cleave, if not just weave in Thrill of Battle + Upheaval to finish the combo. After that I usually just swap back to Defiance until Inner Beast's cooldown is back up to make things a little easier on the healer, but you should have such a massive Enmity lead that if the healer is comfortable you can probably spend the rest of the fight in Deliverance.
[Raids] I wouldn't bother stance dancing when you are still learning raid content, especially in Savage mode. Save it for progression and when you're up against a DPS Check/Enrage, and then do the same as above under Dungeons - Bosses. Stay in Defiance until you're up to 80 Beast Gauge, get to 100 gauge with your Storm's Eye combo, do your crazy Fell Cleave combo, then back to Defiance (unless you're very confident in your healer). If you are planning to spend more time in Deliverance I would make sure your OT knows to use the Provoke + Shirk combo frequently so you don't fall behind on aggro; even with all the Fell Cleaves and the early opening aggro spike it's easy for RDM and SAM to rip stuff off of you if you have to miss a GCD or two when avoiding mechanics.
In general, if you are going to be staying in Deliverance because you trust your Healer, you're going to have basically unlimited TP in boss encounters, so it is still worth swapping to Defiance briefly to pop Equilibrium in a pinch (Saving Equilibrium in OS1 helps a lot after Charybdis so the healers can focus more on picking up the offtank for that upcoming Twin Bolt).