What causes RuntimeError: ERROR 010240 saving after CellStatistics?

Amazingly all my troubles have to do with the lack of gdb use. As soon as I assigned the scratchWorkspace to a .gdb my write errors started going away!

env.scratchWorkspace ="G:\\Faculty\\Mann\\Historic_BCM\\Aggregated1080\\Scratch.gdb"

You should do this (best practice with rasters to avoid unnecessary copying):

env.workspace = env.scratchWorkspace = "G:\\Faculty\\Mann\\Historic_BCM\\Aggregated1080\\"

then you can run

mean.save("outa.tif")

and it will save to that folder. No need to specify the full path, which may be part of your issue.