Is this on a windows or Linx Server as they can behave different even if its the same version of mysql.
As there log files, i assume for tracking,
you should be able to back them up, and then delete them.
As you say starting a fresh with a max log size.
I don't know for sure as the versions and platform can be important.
But even if you answer those questions, i don't think i could
give you a 100% Answer.
Don't forget, if its not broken dont fix it