let's just say that heiji got shrunk alongside shinichi (the lore is up to you, maybe he wanted to find shinichi earlier so he followed him at the tropical island or something)
how he's going to deal with his own alter ego?? since shinichi is different from him how is he going to feel that his own alter ego is slowly replacing his life??
I think I'll leave lore options aside for a minute. (Because Heiji's reason for coming to Beika is because Shinichi vanished, Kogoro started to be the one making headlines instead, and he came to the agency because his main deduction was that Shinichi retreated into the background and was advising Kogoro on cases. He wanted to prove he was right, and then it became a competition because he thought that Kogoro would be telling Shinichi about the case that came up. There wasn't really an indication he was planning to head into Eastern territory before then, though reasons could be created.)
If they shrunk together, then Heiji is stuck in Beika, which would be his main issue tbh. He knows Shinichi, because he's the one who compares himself to his fellow high school detective and keeps an eye on his exploits, but Shinichi doesn't know him. They'd still probably end up going to the Kudo house together, because Heiji wouldn't have other options, and they'd both be aware that they barely survived a dangerous encounter. (I don't know if he could make up a name on the fly, Shinichi or Agasa would probably panic pick one instead.) Therefore, it's in his best interest to not return home.
...Which would be a more major problem than when Shinichi went missing. Shinichi's parents have been letting him do pretty much whatever he feels like. It's implied that he travels around at least a bit for cases people request (Shiragami), so it wouldn't be too odd for him to be on a case, and Agasa was there to give a vague explanation why he's not home. But Heiji? Heiji lives with his parents, his mom fusses over him, his dad is freaking police chief in Osaka, so if he's missing, there will be a search. He's also the captain of the kendo club (meanwhile Shinichi isn't in a club at all), and his absence will be immediately noticed. For Heiji's child identity to gain...well, an identity, he's have to first make sure that his parents, police friends, schoolmate, or Kazuha don't even see him, because they have a much higher chance of understanding that the random dark-skinned Osakan boy hanging around Beika for some reason is a little Heiji than anyone who ever suspected Conan of being Shinichi. There is so much higher of a chance that the story is going to be that Heiji's family finds out and steps in to investigate the men in black and be very police drama, even if neither of the boys want major involvement.
But. In the rare chance hypothetical that Heiji can be a tag along for the normal events (slightly altered, maybe Kazuha barges into the agency instead because of Kogoro gaining a reputation in the same area Heiji visited when he disappeared) of canon... There's a few phases he'd probably go through.
1) Hey, now that we're in the same boat, I can compete with Kudo in these cases that pop up. (The two of them frequently whispering amongst themselves to discuss the case when the adults make it clear they view them as pests, eventually becoming interested in whatever they're focused on as more cases happen because lbr, one boy is easy to ignore and let wander around, two boys getting into things and having discussions is harder to not notice. I'm not sure if Kogoro would put up with two people at the agency, he might have to stay with Agasa, but he'd probably hang out with Shinichi as much as possible.)
2) I'm glad I can chill and get cases solved without my dad breathing down my neck about all the wrong ways I'm doing it. ...But I do...kinda miss everyone in Osaka. The kids are fine (he would actually love the little adventures they go on, and isn't a stranger to basic detective requests like lost cats, it's important for the community), and the food here is... okay, but you really need to try this one place-
3) He'd probably view being a child even worse than Shinichi. Even if he gets a handful of friends, he loves his hometown. Shinichi does have a life he wants to get back to, but he at least gets to stay with someone he knows, live in the same town he grew up in, and see glimpses of his other friends from time to time. I can see Heiji having times where he's a lot quieter than we're used to him being. He'd probably be more frustrated about it all, but also more likely to focus on helping Haibara (or annoying her, from her perspective) because he has a stronger interest in the cure. Possibly also more reckless than Shinichi during encounters with the BO, though since both him and Shinichi would be tackling the problems, maybe they'd balance each other out, idk. (He's unlikely to be involved in the train encounter, but ones after that he would.)
Heiji would act pretty much exactly as his usual self, and would probably stumble for a long while on which name he introduces himself with. He's worse at lying than Shinichi, it's not a habit he'd build up easily, and he wouldn't have much interest in hiding who he is when there's no one who really knows him outside of Osaka anyway. His presence as a shrunken child could cause complications to the narrative (Conan can fly under the radar, but two little detectives popping up when the teens disappeared is easier to see. And the previously mentioned Osakan perception threat to finding out the truth. He's generally the more recognizable of the two teen detectives if anyone had at least heard of the Osakan detective.) but two small detectives would create a pretty solid bond and add to strategies for how to deal with their problems.
If Shinichi's view of Conan could be described as a chronic illness - keeping him from the life he was living and forcing him to adjust to reach the same functionality he had while he hopes there's a way to fully recover - then Heiji's outlook on being a child would be more like a forced exile. Once they set up the voice changing, he could try talking to someone to say he's okay or chat, but there's also a chance he wouldn't take the opportunity, because he wouldn't want to drive anyone to look for him. I'm not even sure if there's a good excuse for him using the antidote, because Shinichi would still be the one to try it first (Ran's close to finding out, the prototype for the antidote isn't even a guaranteed survival), and even if he'd want to try it since Shinichi would be back to normal for a day, I don't think Haibara would let him. She had a good suspicion on how long it might last, and when they both know it's temporary, Heiji would have to really weigh if a single day as himself would be worth it. They both messed up, but he's not allowed to return to his life at all until the problem is solved kinda thing.
...Anyway, that's enough ramble, that should be enough of a gist on how I think it'd go.
