There is probably some kind of easy iteration thing to do in order to get all of this to behave the way you want, but I cannot think of it right now. This may be tedious, but this is what I would do since there isn't a ton of data.
For the first extract folder, export it all into a geodatabase (from ArcCatalog, create a new file gdb and import multiple shapefiles and grab them all from that folder). Then add all those feature classes into ArcMap. Then for each subsequent extract folder, load the shapefiles into the same ArcMap instance, start an edit session for the original gdb features, and copy and paste the shapefiles into the gdb.
I hope that makes sense and it's too bad that Append didn't work. I'm sure someone else on here (likely tomorrow) would have a better and more appropriate answer involving a geoprocessing tool and maybe some iterations. Either way, good luck!
