When loading BYOC, try to drag and drop only the BYOC pk3 onto the Zandronum launcher.
Zandronum should automatically detect the Doom2 wad if it's in the same folder as it.
There shouldn't be a need to extract the files contained in the wad or, in this case, the pk3, this would only break the reading process.
There is a chance that your download was corrupted at some point.
I've downloaded the two different files on my side and these work perfectly fine.
That is the only explanations that came to my mind, I hope you will be able to play our mod.
Maybe try to put the solo pk3 into the all in one file. Maybe that will fix the problem since the pk3 seemed to be broken in the latter on your end.