Well, everyone translates Muraji to be the rank that was then demoted to be SEVENTH out of eight and inserts seventh into that.
But the way I look at it, we can confirm the first is Big Black... But Muraji and tarou are a little vague. If we look at things in total without any attempt on my part to reconcile certain things.
We have Oouguro Rentarou or Daikoku Rentarou, followed by Big Black Muraji Son.
If we look at the more mythical meanings of things, we find that Muraji is "A title for those descended from gods. Other than the ancestral deities of the royal family." rather than some bureaucratic title in the Feudal Era- When we consider that Daikoku is seen as a God of Wealth, but specifically a God of Farming/Agriculture, we can draw direct parallels between him and Hades in Greek Mythology, who was also originally an agricultural deity, but soon came to be associated with precious gemstones and eventually wealth. We can further go towards Daikokuten which is literally a God of Great Darkness or blackness... Also ironically, the God of Five Cereals. It is reeses, but for breakfast, and silly rabbit, tricks are for kids! The other God called Ebisu, was seen to be the son of Daikoku.
Given the themes of blackness, darkness, and sons. We can draw some parallel strings to Ebisu which deserve to be investigated further. Ebisu was a Fisherman like fat man, similar to Daikoku who was also fat and wore a black hat, Ebisu was also banished to an island. Both of them form dialectical parallels as being seen as the God of Earth an the God of the Ocean.
So if we take some liberties we could poetically translate it to be The Eldest Son of the Great God of Darkness given that Muraji can be a title to those who descend from them and Taro is literally son, even a heroic or a masculine son, being the more romantic meaning than eldest son.
To be thorough, you can prefix Taro 太郎 to be Golden Boy or Peach Boy. Both of which are also mythological figures as we can look at Momotaro and Sakata Gintoki (No, this isn't Gintama.)
Momotaro, or Golden Boy, born from a peach, found in a river like Moses, son of the Gods, traveled to Onigashima, a demon island believed to me Megijima in the Kagawa Prefecture. It translates pretty well into female, and has its own twin island, the male Ogijima. On this island lives seven Ogres or devils, Momotaro comes and defeats them, especially their big bad boss, the chief devil Akandoji, and takes all of the stolen gold and silver and (ironically since they have no claim to it) gives it to his foster-parents. Before he confronts the demon, he also befriends three animals, a dog, a pheasant, and a monkey, by giving them some dumplings.
This story was also further popularized after it was used as propaganda where Momotaro and his three friends attack the island and defeat the Demon King, being paralleled to the attack on Pearl Harbor. There is also some correlation of Momotaro "growing up" to defeat the demon king.
As we go to Kintaro, we find that he is a Warrior Mountain-Spirit who was raised by a lone mother in... you guessed it the mountains after his father committed suicide. His mother is also the demon witch Yama-uba who eats people and has silver hair. He grew up to be extremely powerful with animal friends and his ability later impressed a noble named Yorimitsu, who took him in as his retainer. He also killed the Shuten-Doji, a demon terrorizing Mount Ooe. Yorimitsu served as commander of a regiment of the Imperial Guard, and as a secretary in the Ministry of War in addition to numerous other government positions. This corresponds to Heiji's comments about ranking officials in the Japanese Government being in the guest book. He is also said to be the son of the Thunder God, Raijin.
Jurōjin would actually be a better fit for the "immortality" theory as he is the God of Longevity and is normally accompanied by a deer. But he isn't mentioned anywhere...
If we go back to Rentarou, it comes from Japanese 連 (ren) "join, connect", 太 (ta) "big", and 郎 (rō) "gentleman". Ren can also be taken to be clique, party, or gang. We can take ro to be son, young man, or gentlemen so there is not much flexibility there. Ta, can also be the fat type of big.
Given these themes, I will be re-reading the mermaid case and looking for clues.