This is an exact description of what cross-posting does. Think of cross posting as “Automatically taking my Micro.blog post and copy and pasting it into that other service and posting from my existing account.”
It’s not exactly that, because there are some differences in content presentation, but it’s pretty close.
For example, you can see anything I post on json.blog on my account jsonbecker@indieweb.social. I also let people follow my blog directly in Mastodon or other ActivityPub services using json@json.blog. If they reply to my crossposts on jsonbecker@indieweb.social, it shows up in my Mastodon client. If they reply to json@json.blog, it shows up inside of Micro.blog.
You don’t have to choose one or the other, and you don’t have to migrate any accounts if you don’t want to.