First I would like to clarify the title:

A "Harry OC" would be a character named Harry Potter that for all intents and purposes could be named anything else and that wouldn't change much of the story. Examples include most of the independent and/or powerful Harry that begins before Hogwarts as Harry usually isn't raised by the Dursleys and sometimes even manages to get the horcrux removed by Gringotts, healer or something else. (Sometimes Harry will even change his name but it's ok because he used to be called Harry)
A "(not)Harry OC" would be a character that is not named Harry Potter but that is placed into Harry's canon role. This seems rarer from my readings and seems to be used as a way to write an OC that you can still tag as Harry Potter. I think the best example of this is from Harry Potter and the boy who lived by the santi as you could exchange the name of the brothers and the story could be kept the same.
A "Canon OC" would be using any of the named canon characters that aren't really fleshed out to write whatever it is you want.
And a "New OC" is just creating a new character that doesn't appear on canon.

That explained, I would like to ask.
When you search for something to read do you have a preference for Harry OCs instead of New OCs (as do you prefer stories with a main character named Harry Potter even if it's very obviously just a new character that happens to be named Harry Potter)?
What do you think about the whole (not)Harry OC situation and having a character that is basically Harry but not named Harry? Would you prefer just having canon Harry instead and the writer going for a new OC or a canon OC as the MC? Or would you prefer like in the santi story where you have a boy who lived who is (not)Harry and have the MC be named Harry Potter even if he is just a Harry OC?

I'm asking because I had an idea for a fanfiction and had to shoehorn Harry into what I had in mind. Didn't help that I wanted to keep canon happening in the background so I still needed a new (not)Harry OC. It was at this point that I thought to myself why not just make a New OC and let Harry be Harry.

 

I can only speak for myself, but I'd be more inclined to read your example of a Harry!OC than a new OC. I can get around that if there's non-goofy reasons why he's like that.

 

The way I read, I almost exclusively focus on what you've termed as Harry!OCs. I'll be honest, even when an author changes damn near every facet of Harry's personality, it still doesn't feel like an OC to me, provided there is at least some sort of explanation. I see changes to his character in the same way as I see plot divergences- events necessary to create the story you want to tell in the world. A Harry that acts in a different way than his canon self isn't something I'd consider an original character, because so long as he bears the name he's the character to me.

New!Ocs don't tend to go over well with me, and I very rarely will start up a story based around one. Part of this is because they tend to be rather shit stories (either bland or a pure avatar for the author) and part of it is because of the changes necessary to the world to tell a story around an OC. See, if you add a whole new character, and they're the centerpiece of your story, there has to be something special about them. An ability, a high proficiency in some area, a role that only they can fulfill, etc. The difficulty here is that to create a character with significance for the world around them, you often have to change the world around them, as well. That's why so many of the OC's you will see get tossed into a family like the Blacks, or grow up with one or more key canon characters, just to make them important to the war against Voldemort or whatever other conflicts drive the story.

But your situation sounds a bit different. From the brief synopsis, it sounds like you're going for a different, separate plot than the events of canon. This makes it easy for your character to be significant to your plot because the plot is your own, not an already existing one you need to shoehorn them into. I could be wrong here because I don't really know what your story is, but I'd say your two best options are a full-fledged OC, or a non-bwl!Harry who can let either a twin or Neville shoulder the job of Voldemort's nemesis, leaving him free to embark on whatever adventure you want him for.

Either option is viable, though fair warning, OCs tend to be a turn off for a lot of people, and finding a way to manipulate Harry into the protagonist role will probably get more engagement, if that's your first priority.