Well, I've come up with the something, however, this depends on using a .bat file to run the game instead of the normal (last I remember...) launcher route (you could use the launcher bypass or run the launcher exe).
This one requires you to add a folder named "consoleArchive", or whatever name you want for it; however, it must exist before running the code.
copy "console.log" "%cd%\consoleArchive\console %date:/=-% %time::=-%.log"
This code will simply rename console.log files so that they stay in the main Blockland folder instead, so no need for a folder.
ren "console.log" "console %date:/=-% %time::=-%.log"