First of all, congratulations on your team's success on the ladder. "XYZ" or in other words, the Aura Trio is quite an interesting core because you know how much meta-defining they are. Yveltal is something that's almost in every team due to its specially defensive set being mandatory to check Calyrex-Shadow and a solid Defogger, Xerneas also has respectable defensive capabilities and utilities as a cleric while LO Zygarde is a very potent sweeper.
However, there are some flaws which can be seen at first glance.
The first one is that you struggle very much vs Ground-types, primarily Groudon. It can easily set-up a Swords Dance on Necrozma-DM and then it can claim in a few kills until you do a desperate Dynamax, or something like outspeding and using Glare with Zygarde-C and proceeding to revenge kill with Calyrex-S or Palkia. Nonetheless, Groudon is very scary considering your Yveltal doesn't have Foul Play nor outspeeds most of the fast sets it runs.
Kyogre, as you'd mentioned is also very troublesome. Bulky sets mainly can shrug off any damage or status and fodderize most of the team as CM bait. Palkia does not have the longevity, nor the means to dish out enough damage to force Kyogre out after it sets up Calm Mind. Choice Specs set also win long-term, due to Palkia's lack of reliable recovery and constant chipping from hazards. Palkia itself is a very mediocre Kyogre check, easily outclassed by the likes of even Kyurem-White, ignoring the fact that Eternatus is just miles better.
Ferrothorn. This team is total dead-weight when facing Ferrothorn, as it doesn't have any issues against 4/6th Pokemon of the team. Palkia is prone to Spikes and Leech Seed chip and Calyrex-S has the unfavorable scenario of getting Thunder Wave'd or Knock Off'd. Yveltal can not hold a candle to it, and there's nothing that can soak up Leech Seed PP like Eternatus or Ho-Oh does in general.
Geomancy Xerneas and Leech Seed / Baton Pass Calyrex-S are also very bothersome for this team. The former threatens getting a free Geomancy boost on most of the team, which is very concerning. Choice Scarf Calyrex-Shadow lacking Haze fails to stop Xerneas that is not within the range of Psyshock.
Not only that, SubSeed Caly-S has an ugly match-up where your Yveltal can't touch it totally, and in a prolonged stalement it wins due to Yveltal getting Leech Seed' on switchin and everything else fearing to tank a hit from boosted Nasty Plot. Even if you were to try revenge-killing with Caly-S, there's also the risk of the opposing Caly-S Baton Passing SpA boosts to something like LO Yveltal—and against this kind of team, you lack any defensive counterplay and can not make progress in the course of the game.
Both of the above issues can get a quick-fix by adding Haze on Calyrex-S over Draining Kiss, which is most of the time redundant as you're better off using Trick versus Yveltal.
Ferrothorn, Groudon and Kyogre, however need more serious attention and restructuring of the entire team.
NDM (Necrozma-Dusk-Mane) @ Rocky Helmet
Ability: Prism Armor
EVs: 252 HP / 224 Def / 32 Spe
Impish Nature
- Stealth Rock
- Thunder Wave / Earthquake
- Sunsteel Strike
- Morning Sun
This is a minor change, but 32 Spe allows you to outspeed paralyzed max speed Zacian-Crowned. There are no significant changes in defense calculations for shifting out the 28 Def EVs, rest assured. Also, you can switch it to Earthquake in case Zekrom is a problem, but with Scarf Caly-S and Xerneas it shouldn't be much of a worry.
Y (Yveltal) @ Heavy-Duty Boots
Ability: Dark Aura
EVs: 248 HP / 8 SpA / 252 SpD -> 248 HP / 68 SpD / 192 Spe
Calm Nature -> Jolly Nature
IVs: 0 Atk
- Dark Pulse -> Foul Play / Knock Off
- Toxic / Taunt
- Defog
- Roost
Dark Pulse from a slow Yveltal is not something you can count on as enough for Groudon, as there are also faster sets that can just OHKO or deal massive damage to Groudon before you can do something in return. This is not to mention that Kyogre also takes null damage, so you can change that slot without hesitation. Foul Play chunks Zacian-C coming on the switch-in hard, and OHKOes offensive Groudon sets after a SD.
Meanwhile, Knock Off can make Kyogre and Eternatus less worrisome. Toxic imo is fine, and it can also help vs offensive Yveltal sets. Taunt can clutch Ferrothorn at times, so it's also worth. Ultimately, it's up to your preference.
Z (Zygarde) @ Life Orb
Ability: Power Construct
EVs: 24 HP / 252 Atk / 232 Spe
Jolly Nature -> Adamant Nature
- Dragon Dance
- Thousand Arrows
- Outrage
- Glare -> Rest / Stone Edge
The EVs are mostly fine, just slightly optimized to minimize Life Orb recoil. Adamant Nature is also the way to go in my opinion—outspeeding Non-Scarf Caly-S at +1 comes at more risks than advantages, and the significant drop in power is easily noticed.
Glare has no use in this set whatsoever, you already have Necrozma-DM's Thunder Wave for speed control and we just made Yveltal faster for Groudon. Rest has perfect synergy with Aromatherapy support from Xerneas, as it allows you to come on Ho-Oh more frequently without being scared of Sacred Fire burns and gives extra longevity. Stone Edge can also find an use in doing severe damage to Ho-Oh and Yveltal unboosted.
Also if you're that scared of Outrage lock, you can try some other niche options such as Crunch (Lunala), Iron Tail (Xerneas), etc. but it's generally not worth it. You can simply click the Dynamax button and get rid of Outrage lock, or simply reserve it until the Fairy-types have been taken out.
-> 
Eternatus @ Heavy-Duty Boots
Ability: Pressure
EVs: 252 HP / 164 SpD / 92 Spe
Timid Nature
IVs: 0 Atk
- Dynamax Cannon
- Toxic / Sludge Bomb
- Recover
- Mystical Fire
As I've already explained above, Palkia is a very mediocre Kyogre check that also makes you struggle when facing Ferrothorn. Not only that, any physical attacker also does tons of damage and it is not good at soaking Leech Seed PP nor Sacred Fire from Ho-Oh as good as our good ol' Eternatus.
You mentioned that Dynamax Yveltal is one of the key concerns to the team. That's where Eternatus is quite good at: it can easily absorb any of the special Yveltal hits (you have Xerneas for physical sets) and forces it to Dynamax to actually have a chance. Then again, Mystical Fire is quite nasty against such special attackers.
Sludge Bomb can help with the Xerneas match-up—remember that Eternatus lives a +2 Moonblast from non Dynamaxed Xerneas, which can help in scary situations. Heavy-Duty Boots means you won't get chipped by hazards nor affected by Sticky Webs. Eternatus is also good at walling Kyogre and has good recovery.
Xerneas and Calyrex-Shadow have quite fine sets. You could think of maybe making Xerneas Air Balloon with Knock Off Yveltal for Groudon, apart from that it's mostly fine. Calyrex-S should have Haze over Draining Kiss as pointed out before.
Bold: Important parts
Italics: Team changes
Final Team
Hope I was of any assistance, and good luck for laddering further! If you have any questions, please ask.
