Yeah, I think you're spot on. I'm going to shamelessly repost what I wrote in another thread that's focused on the tablets, because I hadn't connected a lot of specifics that you've found.
I've been waiting to read the tablets until I collected all of them. Having done so, I think it does indeed point to his thread being restored.
This is all my interpretation based on the tablets and the ruthless route, but it seems Asterion was given two options to escape. The first would be to take freedom for himself given to him by those who pitied him or regretted their actions. The second would be to right the wrong he was accused of by actually fighting an opponent who wanted to defeat him. The result wouldn't matter, but he absolutely could not back down. However, he would need enough freedom from a master in order to fulfill this, which is why he's never been able to until now. He needed to stay a prisoner of a labyrinth in order to gain freedom and have his ember rekindled from nothing, essentially, and the rules were created to stop that from happening.
I think Poseidon's gift, which relates to what he sees as a moment of weakness when he questions whether he should escape by sea, is a backdoor. A failsafe. I also think the master situation is a cruel repurposing of his refusal to leave without permission from Laomedon, along with his eventual crime.
Your analysis of the specific meanings is great and it's making a lot of things click that I hadn't caught on to.