Healing 446848
Preservation is incredibly good at dealing with this mechanic, both hero specs can handle it very well and while Flameshaper is much easier to execute this on Chronowarden has a higher healing potential for it.
As Flameshaper
Your response to 446848 is your stasis with two engulfs. You should prepare coy and tc before the boss starts running towards the container and then as the cast begins you can start the stasis, use db and then one engulf. Once the second wave of absorbs come out you send the second engulf and then hold the stasis release until the end of the cast so the two consumes that come out of it clear all of the remaining absorbs.
There is a couple of things to keep in consideration when playing Flameshaper here: First is that because the containers happen approximately 2 minutes and 50 seconds between each other, you have to hold your stasis for each container and can't use it in between. There is potentially an angle where with good enough play you can use flow to squeeze that extra stasis out in between containers but the timing is very tight and requires you to play into flow uptime heavily.
Another thing is how stacked your raid gets during the actual 446848 cast. consume only has a 25 yards range around the engulf target so if your group is heavy on ranged dps and they don't get a bit close to melee during the channel or you aren't playing into getting your db on yourself so you can stand in the middle you run the risk of having a portion of your raid out of range of consume which completely ruins your ability to effectively heal the containers.
As Chronowarden
Because of tempburst granting extra cdr you can fit your stasis in between casts of 446848 and still have it ready for a big raid-wide lb with ec without having to actively waste mental space playing into flow. ec itself is also being reduced to fit into the timings of the fight by flow and tempburst.
Your game plan going into the fight would be to cover the whole raid in echo at the start of every 446848 cast and then lb into ec near the end of the cast to clear all the accumulated absorbs. For the first cast you can start the fight with two tas already stored into your stasis and then cast a third one a bit later, followed by releasing the stasis into the raid which would spread another 15 echoes giving you raid-wide coverage
For the following canisters, you can't store three tas into the stasis but you can still get bigger coverage by storing one ta, followed by a single echo and then using chronof on the boss until ta comes off cd. After that you would cast this ta and instantly release the stasis. This will send three tas into the raid while the echoes from the first cast haven't expired yet.
440421
Breaking eggs requires extra healing on 8 targets separated by approximately 45 seconds between each set. While this timing does mean you get an engulf charge as Flameshaper for each, the spell is not really good at doing concentrated healing on priority targets. If more priority healing is needed on these targets your best bet is to manually echo them and lb. If they are well covered then you just do your normal priority of spreading echoed revs and dbs on the group.
Chronowarden is better at healing people breaking the eggs with 440421 as your lb is much stronger thanks to afterimg and overall your healing outside of containers should feel way better. This combined with the higher burst generation means its easier for you to have enough resources to cover this mechanic.
Assuming a skilled enough player to properly execute Chronowarden on this fight, i heavily recommend the tree as it just has so many strengths that make it more useful for a team progressing. But in other situation Flameshaper is still a very strong pick for the fight while reducing the mental load required to play the fight by a lot.