Questions on list and Canticles

I have a question about Canticles that might sound a bit stupid, so I apologize. If I'm not mistaken, in the Index, when we use Canticles, regardless of whatever forge world our Detachments belong to - so even if I take one Draconis IV forge world Detachment and ally a Mars/Ryza Detachment to them, I pick one Canticle and it applies to all my units with the Canticle ability regardless of forge world. Is that correct?

For example, I have a Draconis IV forge world Battalion Detachment of 2 Tech-priests Dominus and 2 Skitarii Vanguard squads and 1 Skitarii Ranger squad, and 1 Mars forge world Spearhead Detachment of Belisarius Cawl and 3 Onager Dunecrawlers and 4 Kastelan Robots with a Cybernetica Datasmith. Say I use a Canticle, all of them get it, regardless of whether they're Draconis IV or Mars, right? If I use Shroudpsalm, everyone gets it?

Now, the problem is if we use the new rules in the codex. Let's say I pretend my Draconis IV is Ryza or Stygies VII because I want to use their dogma and Stratagem, but ally them to Belisarius's Mars Spearhead Detachment. But Mars forge world dogma is pick 2 Canticles randomly and all Mars units gets both benefits. So what happens for my Draconis IV/Stygies VII Detachment? Do I roll for their Canticle separately? Or do I pick one of the Mars Canticles that I rolled earlier and use that for them?

Well, I hope someone has an answer. For now, I'm just playing Mars forge world and assuming my Draconis IV uses the Mars forge world dogma, rules and Stratagem. And that Belisarius Cawl is another character who uses the same rules, but is an Archmagos of Draconis IV.

Speaking of which, I've been crafting a couple of lists to see what works for the new codex and Stratagems. So they look like this:

Mars (Draconis IV) Belisarius Cawl, Tech-priest Dominus, Tech-priest Enginseer, 2 5-men Skitarii Vanguard with 2 plasma calivers each, 2 5-men Skitarii Rangers with 2 transuranic arquebus each, 4 Kastelan Robots with 3 heavy phosphor blasters each, 2 Cybernetica Datasmiths, 2 Kastelan Robots with incendine combuster and Kastelan fists, 2 Onager Dunecrawlers with neutron lasers and 1 Onager Dunecrawler with Icarus array.

Stygies VII (Draconis IV) 2 Tech-priests Dominus, Tech-priest Enginseer, 2 5-men Skitarii Vanguard with 2 plasma calivers each, a 5-men Skitarii Vanguard with 2 arc rifles, a 5-men Skitarii Rangers with 2 transuranic arquebus, 4 Kastelan Robots with 3 heavy phosphor blasters, a Cybernetica Datasmith, 2 Kastelan Robots with incendine combuster and Kastelan fists, 2 Onager Dunecrawlers with neutron lasers and 1 Onager Dunecrawler with Icarus array, and 3 Sydonian Dragoons with taser lances.

Stygies VII (Draconis IV) with House Yato Knight 2 Tech-priests Dominus, Tech-priest Enginseer, 1 10-men Skitarii Vanguard with 3 plasma calivers, a 5-men Skitarii Vanguard with 2 arc rifles, 2 5-men Skitarii Rangers with 2 transuranic arquebus each, 4 Kastelan Robots with 3 heavy phosphor blasters, a Cybernetica Datasmith, 1 Onager Dunecrawler with neutron laser and 1 Onager Dunecrawler with Icarus array, and 1 Knight Warden with twin Icarus autocannons and meltagun.
Or:
2 Tech-priests Dominus, Tech-priest Enginseer, 1 10-men Skitarii Vanguard with 3 arc rifles, a 5-men Skitarii Vanguard with 2 plasma calivers, 2 5-men Skitarii Rangers with 2 transuranic arquebus each, 4 Kastelan Robots with 3 heavy phosphor blasters, a Cybernetica Datasmith, 2 Onager Dunecrawlers with neutron lasers, and 1 Knight Warden with twin Icarus autocannons and meltagun.

Or:

2 Tech-priests Dominus, Tech-priest Enginseer, a 5-men Skitarii Vanguard with 2 plasma calivers, 2 5-men Skitarii Rangers with 2 transuranic arquebus each, 4 Kastelan Robots with 3 heavy phosphor blasters, a Cybernetica Datasmith, 3 Onager Dunecrawlers with Icarus arrays, and 1 Knight Paladin with Stormspear rocket pod. Can use 2 neutron lasers if I swap the Stormspear rocket pod for twin Icarus autocannons.

Mars with House Taranis Knight (Draconis IV with House Yato Knight)

Belisarius Cawl, Tech-priest Dominus, Tech-priest Enginseer, 2 5-men Skitarii Vanguard with 2 plasma calivers each, 1 5-men Skitarii Vanguard with 2 arc rifles, 4 Kastelan Robots with 3 heavy phosphor blasters each, 1 Cybernetica Datasmith, 3 Onager Dunecrawlers with Icarus array, 1 Knight Errant with twin Icarus autocannons.

Mars (Draconis IV) Belisarius Cawl, 2 Tech-priests Dominus, Tech-priest Enginseer, 2 5-men Skitarii Vanguard with 2 plasma calivers each, 1 10-men Skitarii Vanguard with 3 arc rifles, 1 5-men Skitarii Rangers with 2 transuranic arquebus, 3 Kataphron Destroyers with plasma culverins and cognis flamers, 4 Kastelan Robots with 3 heavy phosphor blasters each, 2 Onager Dunecrawlers with neutron laser, and 1 Onager Dunecrawler with Icarus array.

Mars with House Taranis Knight (Draconis IV with House Yato Knight) - my personal favorite Belisarius Cawl, a Tech-priest Dominus, Tech-priest Enginseer, a 5-men Skitarii Vanguard with 2 plasma calivers, 1 5-men Skitarii Rangers with 2 arc rifles, 3 Kataphron Destroyers with plasma culverins and cognis flamers, 4 Kastelan Robots with 3 heavy phosphor blasters each, 2 Onager Dunecrawlers with neutron lasers, and a Knight Paladin with twin Icarus autocannons. I can swap the Onager Dunecrawlers' neutron lasers for Icarus arrays, and change the Skitarii Rangers to Vanguard, so that I can swap the twin Icarus autocannons for a Stormspear rocket pod.

I don't which is better and I have no idea what to do. What I do know is that I don't have any Sydonian Dragoons so I'll have to buy them if I go for the first Stygies VII list. Oh, and I also don't have the Kastelan Robots with incendine combuster and Kastelan fists either. Oh well. Well, the second Stygies VII list seems doable. I think.