Splitting some of the parts into smaller parts will expose the insides to outside air which brings some serious cleanliness issues. The mirrors especially will get destroyed instantly by heat if there is any dirt on them when they are flashed by EUV.
I imagine they do the disassembly and packaging in a clean room. (At least for now the technicians require air :D) Then the packages are vacuum pumped, sealed, then shipped. Then at the destination fab they are assembled again in a clean room.