I'm starting to think with the length of the stranding you're going to have to phase into what the Ravenguards did after Horus broke them. Your existing armor is even more precious so the growing reliance on light infantry might be better for the task ahead.
Depends what you're going up against really. During the End Times the Lizardmen bring out all their Cool Stuff, so if over time I escalate the game stakes, for example the stuff I was mentioning about Elven reformation, or Dwarves rediscovering stuff, this is all items which once saw off a tide of daemons. Compare, for example, an Empire army of basically just 2000 dudes with spears, maybe a few canon etc, against a squad of Space Marines. Except perhaps for a direct canon strike point blank to their head, nothing in that army will harm them, they'd just wade through any resistance, so yes, lightly armed and armoured marines would be fine, backed up by PDF style soldiers with autoguns and artillery.
Comparably though, if you escalate the stakes, you might get Dwarves for example with a load of runes on gromril items that would let them go toe-to-toe with Marines in Power Armour, in that case, lightly armoured Marines would indeed get killed, that's when you might start bringing out the heavier equipment again like tanks.
Again, as mentioned in the threadmark, you can make more armour whenever you like with actions, and direct the Armoury to produce X equipment. However, if, for example, you want to reserve Armoury time for producing more exotic items, or recreating your Thunderhawk fleet given it's been damaged a lot, you could make a Infiltrator Armour factory which could autonomously produce such armour, because it's simple enough to make without a techmarine making each bit by hand.
Currently this is basically a policy decision, so go with whatever feels best at the moment, and later you can decide differently if you like.
Assuming initiates die every time the person training with them does feel really weird but still strikes me as an improvement over our original policy. Wouldn't it make more sense to instead have large maluses applied to rolls for their survival?
Depends what you mean by improvement. In theory, having individual training would increase the odds of scout survival, but you'd also get the situation of marines going into dangerous battles with incompletely trained scouts next to them. You couldn't just leave the scouts behind because they wouldn't accept that culturally, and the whole point is to have them by their trainers' sides. Comparably, 'centralising' the training and having scouts trained in the 10th Company as usual means they work their way up in experience and intentionally aren't deployed in more dangerous situations. In the first case, you can train more them, distributing the burden of training across the chapter, and there's a legit point to be made that training a lot of scouts at once really saps the Chapter's veteran expertise. Instead of deploying them to fight you have to have them back doing training.
Also, re rolls etc, I don't want to keep track of each scout primarily for my own sanity in updating numbers. There's increased danger of me making a mistake somewhere and it throwing all the numbers off. I'm even a bit skeptical of tracking individual suits of power armour for example. BUt yes, some of this is flavour, some of it is just me trying to make it easier to run the game
Like I find the risk of alienating the company acceptable because we've already alienated reclusium if both groups think leadership is trying not to play favorites surely that can only help?
So a few points to keep in mind here.
Firstly, The Reclusiam isn't necessarily 'alienated'. they acknoledge that the Chapter is in extraordinary circumstances, they're very concerned, they've been taking certain actions to reduce their concerns, eg destroying certain artefacts without consulting anyone, but they're not actively hostile. They are the internal affairs of the chapter, this is after all their job. However, they're still on board with what's going on, even if they're actively trying to spread their influence through the Companies.
Currently in the chapter you've basically got a traditionalist wing, led by the chaplains, some of the veterans, and so on, and then you've got a more 'modernist' (bad word choice but sure) faction largely made up of hte Librarium and sort of the Apothecaries. The armoury aren't really taking a side, and the Captains are largely favouring the Reclusiam. Again, this isn't really a problem. It's the Librarium's job to investigate weird stuff, it's the Reclusiam's job to maintain the Chapter's traditions. The correct functions are being fulfilled.
The Pyrocults meanwhile are present already, in the population of chapter serfs, and in some of the marines (if they weren't mind wiped of it). The cults value personal independance, individualism, heroism, sacrifice, 'progress making' eg building and going out and doing stuff. Comparably, the more orthodox Imperial creed is xenophobic, defensive, traditionalist, heirachical, fearful, dogmatic and crushing. The pyrocults for example would be great for producing prideful, valiant people, but the traditional Creed is far far better at producing menials to work in the Toxin Mines for 16 hours a day and meet daily quotas etc.
As noted, this is a largely flavourful choice at the moment, Confessor Hermina for example isn't going to instantly rebel if the marines start spreading their own version of the Imperial Creed, but it should be noted that she has a plan as a Missonia Galaxia operative.
Kaaram, after his magical experience at the Fulgurite Field, now wants to go and preach his childhood religion., he thinks the burning soldiers he saw have blessed him, which they may or may not have done. This isn't offensive or forbidden, it's a bit weird and it's not really the Marines jobs, so if it spread through the chapter you might see more preaching or more engagement with religion of the Mallusian natives, but the Chaplaincy know the pyrocults are a thing, a lot of them would be also been inducted in their youth, they're not going to be that concerned about it.
I've also done it to provide potentially interesting scenes in future chapters. The Sigmarite religion, for example, has a variety of branches, if you interpret Sigmar-as-Anvil, that's all about defensiveness, bearing wounds and hardship nobly, obedience etc, whereas Sigmar-as-Torch is about his light bringing and civilisation making. As such there's a lot of literary fodder there for creating a unique culture for the Celesial Lions.
Oh and before I forget, there's also potential advantages in establishing a unifying internal Chapter religion given the injections of utterly foreign aspirants. If you recruit from Imperial worlds, even feral or feudal ones, you can rely on not having to teach people the Emperor is awesome etc, whereas here you're recruiting people who've never heard of the Emperor. Again the Reclusiam is dealing with this, but reviving the pyrecult stuff might be cool for that reason
So what equipment problems or other issues would the other Imperial factions have while the space Marines aren't in charge of them?
So the Mechanicum are largely focused on setting up your tech base, doing resource extraction etc. That will solve your problems of supply (or at least mitigate them), but meanwhile the people of Araby are starving to death, all their rivers are clogged with sand, their farming has been devastated, and various other problems are about. You could, for example, have the Mechanicum create some desalination systems for them, to provide water, you could direct the Mecanicum to building hospitals or aqueducts, producing vaccines, etc etc. All of this comes at a cost, your resources aren't infinite. Comparably, there's specialist uses. The Soroitas want to create a new priory and are training women, but they only have a few suits of power armour. If you wanted to create such a force you'd need to get someone to make some Soroitas equipment. Stuff like that really.