Local network emulation has always been a bit spotty. While it should work, it's nowhere near as reliable as actual online stuff. And there isn't really a known good solution to this, either.

Since you're on emulator anyway, it would probably be easier for now just to extract the to be migrated pokemon from your generation 4 save file and inject them into your generation 5 save file. I understand that may not the most desirable solution, since save editing by most is considered a cheat, but it is also not exactly the worst thing you can do; a lot of competitive players just use generated pokemon that were created with the same tool, anyway, and it's been considered "legal" for most events as well.

As for the right tool to use, I personally have the best experience with PKHeX. It is the most up-to-date tool with support for pretty much all Pokemon games, and allows you to export individual Pokemon to a file to be reimported elsewhere. Even in bulk.
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