You use this tool (JK save manager) to transfer everything for Streetpass Mii Plaza (Boss, ExtData, and system save data). Since you are doing Activity Log, you also transfer all of those that exist for Activity Log. I would recommend transferring Mii Maker, since you'll lose your Miis on the new machine anyway.
Then go get extdata_dump at
http://gbatemp.net/threads/3ds-extdata-dump-and-restore-tool-extra-data-editing.378492/ , and put it in your 3ds directory for use by Homebrew Channel. Run it and dump all the extdata. Go put extdata_dump on your new machine, and copy everything from F000000B from the old machine, except the gamecoin.dat into your new machine's extdata_dump directory. You should have the idb.dat, idbt.dat, ubll.lst, CFL_DB.dat, and CFL_OldDB.dat listed under F000000B at
https://3dbrew.org/wiki/Extdata#NAND_Shared_Extdata . Create a config.txt with a line to load each file (I forget the syntax offhand) and load it on the new machine.
I don't know which of those files you actually need. CFL_DB.dat is the Mii database; one or more of the others is the title icons database. Because the Mii database and title icon database are used by other programs, you can't do this without affecting the other programs, in particular Mii Maker and Activity Log. You are trying to copy Activity Log anyway so that's okay. Nothing can be done about Mii Maker short of copying all the Miis to the source system first in the normal way (so they'll be in the database when you copy it back).
Once JK Save Manager gets the ability to back up and restore this data, you won't need extdata_dump.
Also, Mii Maker seems to recognize the original creator of the Miis as still being your old machine, so you may need to create a new Mii to use when those are not allowed.