1. Ultramarines could canonically be convinced to let aliens bring their leader back to life. They're hardly something that we have no options of going through. I think noting them as a "problem" is spurious and overly pessimistic.
2. It's just a Chaos sword. Transcendent Alpha trumps that. Maybe if it was something like Drach'nyen but the Anathame is super far from being anything like that.
1. Canonically they were desperate, the shrine was going to be over run anyway and the people convincing them to open up with the Eldar were Saint Celestian, Inquisitor Greyfax, Archmagos Cawl with the Armour of fate and Grey Knights. This is not canon. We maybe able to get in, but I'd wager Lin and the Primarch's will need to vouch for her at a minimum.
2. Andres logic. A "mere" chaos blade is not enough to put a Primarch on the brink of death with a single cut. It requires a planet exploding in their face to send them into a coma and they pick themselves up after being shot in the face with titan scale plasma guns (and that was Lorgar the physically weakest Primarch), and Anathame required the chaos god's themselves to heal him. Maybe it might have been avoided if they had Librarians, but either way a single cut from the whole blade was all that was required to bring Horus to the brink of death. Even when it was young it was "no mere chaos blade" and can you think of single more important artefact than the sword that started the Horus Heresy? Maybe the Golden Throne, but other than that? So I'd say it's fair to say that it's been enhanced by 15 thousand years of influencing the galaxy due to that one action.
If you need any more proof Anathame is also the only other weapon in setting that I know off that can perform a similar "cutting into and out of reality" thing as Drach'nyen. In fact they seem to be able to do it on a much wider scale, a single shard letting an entire ship translate to the Warp without needing to do normal calculations or even charge it's warp drive. Again normal chaos blades do not do that.
Additional proof of how hard it is to heal is that the Eldar are actively looking for a way to do just that, but they haven't found a way and they have...well more everything. Skilled chronomasters, dedicated healers and at least 2 active gods and they can't fix it.
fakedit: Looking at Lexicanum more it doesn't seem like the Anathame was even used against Guilliman. It just said Fulgrim stabbed him in the neck with a poisoned blade. Neither the Anathame's page, Fulgrim's page, nor Guilliman's page say he used the Anathame to do that. Just a poison blade.
Actually I can explain this.
Erebus shattered Anathame, to spread its power to more people, Bile got his hands on a shard with he gave to Fulgrim.
Fulgrim used the shard to ascend to Daemon hood in Angel Exterminatus, but he kept the shard, which he later used to stab Gulliman in the neck (can't remember exactly where it was said, but I'm pretty sure it was said somewhere.)
This is important, because the other shards, Athame were held by Erebus and his followers (several have gotten all over the place by now). In this case, the shards seem to be less powerful than the original blade, as Erebus decided to corrupt Gulliman with it like he did Horus, but only lightly stabbed him. The Primarch resisted a non fatal, blow, but it was close.
However, at the battle of Thessala where Fulgrim laid him low, Fulgrim attacked that same spot that Erebus had hid centuries earlier, which was permanently weaker, but he also aimed to kill with his anathame.