Do you think there are insanely few couples with Percy in this fandom? Characters that are well thought out and have a backstory. For example, Rachel and Percy are an interesting dynamic and a repetition of the Theseus myth with a different end to the story. Or Percy and Michael Yu (Apollo's son who fell off the bridge) It would be interesting if he survived: Percy feeling guilty for the fall, and Michael comforting him. Or Will and Percy, where both feel the guilt of the survivor (Will is the doctor, and Percy is the commander and leader), or the same Percy and Nico with their story and attempts to talk. Percy and Ethan would be a real pain in the ass with a story and explanations. But they don't nominate them as a couple? Like Pernico, they can be found, but everything else? Will's only fanfiction/The Percy I found was the one where he cheated on Apollo with Will, and Will cheated on Nico with Percy. And I really can't stand cheating.
It's a general problem in the fandom, especially prominent in Percy ships, which is that there are very few of them, and it is made to seem that liking any Percy ship other than Percabeth is taboo. It's only recently that there's an influx in other ships, and even that is miniscule in comparison to the excessive Percabeth fic pool . I know how bloody frustrating that is. For a good amount of time, I have vented over that.
Another problem along the same lines is fanart. There's extremely little fanart on any other Percy ships barring Percabeth. This has created a very toxic sort of environment in the fandom for alternative shippings. It also discourages people from making other fanarts and fanfics due to certain toxic Percabeth fans. ( I am not saying all just most of them). Hence why you won't see much material on most of the ships you have mentioned.
I think the fandom has forgotten that people can ship whoever they want, canon or otherwise, and that's the point of a fandom. We are allowed to disagree with the canon and dislike cause in the end books are subjective and we can choose to like and prefer whatever interests us as a reader and there is ABSOLUTELY NOTHING WRONG WITH THAT! Especially to Percabeth stans and recently Solangelo stans, you have your ship, no need to force it on everyone else, sure you can make points about why it's good or why people should like it but that doesn't mean have to or should.
You can dislike a ship and even express why you dislike it, but you can't tell people what they can and can't like. Just give your opinion, try not to be negative or offensive , just stick to the facts and objective reasons why you dislike it or just say it's a personal preference .
I personally generally either favor Perachel or Percy with no romantic partner. But I have read and seen some other Percy ship fanfics.
Perpollo and Pernico are kind of popular and I have read some fanfics of that category though Pernico's popularity suffered greatly due to Solangelo stans as such and some other opinions. (I have covered my thoughts on both Solangelo and Pernico in an old post of mine so check that out if you want).
Other alternative Percy ships I have seen mostly are Percy/Jason or Jercy. I kind of like where thea are going with it cause I really liked Percy and Jason's this odd but very unique dynamic they have and I really wanted it explored more but after the events in HoO and TOA and what happened to Jason( I refuse to accept it still due to no actually compelling and necessary reason behind it plot wise or character development wise), I kind of gave up on it. I really thought Rick Riordan would flesh their dynamic out more thoroughly other than whatever misguided rivalry he was trying to stoke between them. (Let's just agree that despite minor envy they might harbor for each other, they have much higher respect and admiration between them).
There's I think a few who consistently ship Percy and Artemis I think? Which I really thought was very contradictory and just simply not viable in canon or by fanfic cause Artemis is a maiden goddess.
There's Perclarisee which I mean I am neutral on it. I can see what it's based on but I actually liked Clarisse with Chris and I kind of thought of them better of as good friends who bicker a lot( I have a post on Perclarisse as well).
I once made the mistake of searching all Percy ships on ao3. It's safe to say I will never be doing that again ever. The absurd and deranged pairings I saw. Not even bleach will get that out of my eyes or mind.
As for Michael Yew, I am not sure about a romantic pairing of him and Percy, but in an au, it can kind of work, I guess, but I just don't see the appeal. I mean one moment of trauma bonding can't be the basis for a whole relationship.
As for Will and Percy, I see the parallel you are trying to make, but Percy can heal himself, so he's not really in need of a healer most of the time. Cause his power and ambrosia fix most of his injuries. Overall, I just don't think they are very compatible, but I will try and find fics about them for you.
Ethan and Percy? Where the hell did you find that? I don't think anyone ships that. Percy should have killed Ethan the first chance he got. That bastard really really had it coming. Even after Percy spared him so many times, he had the audacity to try and kill Percy. Absolutely not a pairing.
This is like the people who ship Percy and Luke. There are some, and I have never understood it. Luke tried to kill Percy multiple times and showed no remorse for it, and Ethan is the same. They are enemies, not a pairing. Not everything has to be enemies to lovers. But I suppose to each their own, everybody has their own preferences.
As for cheating , to whoever wrote that fic, stay the hell away from pjo respectfully cause neither Percy nor Will would ever do that to anyone. This literally goes against their very nature itself. To people who write cheating Percy fics, his fatal flaw is literally LOYALTY, what the hell is wrong with you?
Anyway, I am very sorry for this devolved into a rant. If I find any Percy and Will fics, I will reblog this post with recommendations.