Oh wow. That's a dang lot you've made me think about. I commend you for your eye for details, good sir.
That bedrock is shown to be far more significant, as you have presented in the instances above. I've never thought of that link between the ichor-made constitution and the bedrock. Your first and second quote I did know about, but I dismissed the bedrock to be nothing more than a metaphor. The third quote, in comparison, is more incriminating. I've finished the ruthless route, but definitely missed the detail of the artifact coming from the bedrock itself. Whatever that artifact was, it is likely related to ichor (also resembling the bedrock's obsidian) and had the power to produce an effect that violates the labyrinth's constitution.
With this, let's make a theory and their implications:
Hardened ichor is the format of the Labyrinth's constitution, and is found in the bedrock
By the gods' combined ichor the Labyrinth is created, a prison for those deemed eternally unworthy of respite. Through their ichor each god is allowed to leave a living legacy in the realm.
You can interpret this as their hardened ichor forming the contract/s that consequently made the labyrinth into existence. If Asterion's blood can harden as such, perhaps he can fashion something to exert his will upon the labyrinth. Though only being part divine, the volume of blood he'd have spilled over the years would suffice, no? He's been tortured over the years, wine and natural regeneration here and there.
Asterion of Crete, adopted son to King Minos, and every drop of his blasphemous blood is hereby sentenced to the Labyrinth.
If the constitution is indeed found at the bedrock or at the least can be interacted, accessed or affected within the labyrinth, perhaps Asterion can append/overwrite it with something of his own design.
If this is true, why hasn't Asterion tried to do this before? Perhaps the years of torture and servitude have made it so that the thought hasn't crossed his mind once to even start thinking it. He confessed himself that he was deserving and a 'wretch' as he describes it. Additionally, what if he can't because he hasn't truly contributed to the realm like the other gods?
In accordance with the hybrid's trial the Olympians staked each a drop of their ichor. One by one each deposited their power on the threadcutter's rhyton. From this shared bounty the realm is created to imprison the damned hybrid and all the Olympians deem guilty of the most reprehensible crimes against divine order.
Perhaps he needs to make the proper offering on the 'threadcutter's rhyton' to make his additions to the realm. I do not conclusively know what this thing is, but I have a morbid idea. It may be Asterion's severed head (idk if he needs to be beheaded to qualify), or something fashioned like it. I interpreted the threadcutter to be Asterion himself, and that's where it lead. Try and look up 'rhyton' and 'bull rhyton' and you'll see what I mean.
Also, a very dark theory: In the ruthless ending where Dominikos takes Asterion's place as the Prisoner, what if it was actually Asterion exerting his power over the realm? Asterion is fixated on the repeating pattern he has seen in his life:
In freeing a prisoner, the redeemer takes on his shackles.
What if Asterion (sub)consciously willed the realm to make Dominikos the new prisoner? After all, this on the route where Asterion did not express pity (he was consumed in outrage) on the Argos's act.