It's been so long since emummc was a thing, so I don't know if this is even relevant anymore, but have you read through the thread :
https://gbatemp.net/threads/how-to-setup-atmosphere-emummc.541060/page-14 ?
Maybe that will help (the bit in the OP about the 1024.bin). I do vaguely recall having issues initially with things installed under SX, but have had none since, so it either got fixed in boot.dat somewhere along the way, or in a newer version of SX Installer.
So, you may very well need to reinstall everything (shouldn't mess up your saves, but backing them up and reinstalling them should work). To test, install a new game using Tinfoil while using SX, then a different game while using Hekate/Atmosphere (both while in emummc), and see if those games run under the different CFW. If they do, you're chasing your own tail here, and the problem lies with how SX originally did installs. Different keys or something silly. In this case, remove the installed games, then reinstall them. No need to keep rebuilding emummc from scratch.
EDIT: relevant thread here if those were originally XCI files:
https://gbatemp.net/threads/atmosphere-unable-to-play-installed-xci-games-from-sx-os.547267/
I've used mostly Tinfoil for a while now when installing stuff. Using Nut over USB for large games and xci files, even.