Disclaimer: This idea of mine hasn't really been done before I think, or rather, if it has it's never gotten enough traction to make people talk about it online.
So the story goes like this, when Zouken realizes that Shinji can't do Magecraft, instead of trying to find a way to mold him into a tool he can use, he decides "Fuck that noise" and tries to "Take care of him" before The Mage Association realize that The Matou family has no legitimate Heir. Cue, you guessed it, Zelretch deciding that Shinji is a worthy candidate for his next greatest Experiment, a spell that cannot only send someone or something to another dimension, but also bring said someone/something back after a specific time after the spell has been cast. Zouken, seeing this as a Win-Win scenario(And having no other option but to agree or face True Death), hands Shinji over to Zelretch.
Bad News, Shinji gets sent to the world of Dragons Dogma: Dark Arisen.
Even worse news, Shinji ends up becoming The Arisen.
Good news, it worked(The Experiment).
Even better news, Shinji not only defeated the Dragon and regained his heart, but without Zouken's influence he grew up to be a genuinely good person!
Unfortunately, he's not exactly all that enthusiastic about being ripped away from his Duties to Gransys, and he's not exactly alone, either.
Now onto the Nitty Gritty.
Shinji is older than in Canon(He's around 23 now), as time moves differently between Gransys and the Type Moon verse.
Shinji got the Best Achievable ending in DD:DA, and did in fact sleep with the king's wife... multiple times in fact. It was consensual on both sides though, which is probably something no other Shinji can say.
Shinji is a Mystic Knight, and has all the abilities from the Mage, Fighter, Sorcerer, Strider, and Magic Archer Vocations(The Vocations are also all at max), although he'll mostly be using Mystic Knight abilities and Enchanted Swords and Magic Shields.
Shinji is Max level, and his Pawn came along for the ride(they were out hunting a Chimera when the "Return" part of Zelretch's spell activated, but no worries it's dead.
Shinji has completed BBI(Bitter Black Island) and all the Side Quests in DD:DA, but only has access to 8 weapons(Enchanted Sword, Enchanted Short Bow, Enchanted Daggers, Magic Bow, Enchanted Shield, Staff, Archistaff, and Magic Shield. Shields of both types(Normal/Enchanted and Magic) are considered weapons in DD:DA for some reason) and 3 sets of Armor. They're all GF(Gold Forged) too, for that extra little bit of protection and strength(Just pretend that there are a lot of Dragons in Gransys that came out of hiding once The Dragon was killed).
Shinji comes back about 3 months before the Grail War, and has very vague memories of his life on Earth(He can't speak any of the languages at first because of how long he'd lived speaking completely different languages).
Shinji has no interest in the Grail beyond the fact that it "Supposedly" grants wishes( He's extremely sceptical about the Grails wish granting abilities), although he will get involved in the War just to keep it out of malevolent hands.
The Mage Association immediately slaps him with a Sealing Designation once he gets back, for very obvious reasons(He basically has access to watered down True Magic, not as good as some of the good stuff, but definitely on par with Low Rank True Magics, somewhere around D Rank True Magic maybe?). Of course, Zelretch runs interference for him, mostly because he actually survived, neigh thrived over the course of his experiment, but not even Zelretch can be everywhere at once, and Church officials and Free lancers don't exactly take orders from him either now do they?
Archer straight up wants to kill him as much as he wants to kill Shirou, as does Alaya.
Sakura is about as traumatized as she normally is in canon, more so due to the fact that Zouken had random people perform the deed on her in order to feed the Crest Worm inside her. Rin and Shirou are much more involved in her life now though, as are Taiga and Raiga(Raiga doesn't take kindly to Pedos and Child Rapists in his organization, and low level mooks are notorious for bragging about anything and everything to people who'll listen, to their own detriment).
His Pawns Vocations and Equipment I leave up to you, and if you want you can give them GF Equipment too.
And that's it. Ever since I watched a playthrough of Extra i've wanted to see what a version of Shinji that wasn't a horrible excuse for a Human Being was like, and now I have the opportunity to show others how i'd like that version of him to be, minus the whole "Arisen!Shinji" thing i've created here. Hope you writers out there can make something decent out of this.