I would like to find a way of running the printer with as small log file as possible (first run after buying as an ideal).

Then I would inspect the file after as least of log data added as possible but bigger then zero. At least it is important whether the increase of the log file alters any previous-written info (if there is some alters then the cryptography might be more complicated).

If there is no altering of previous data the next step is to attempt to achieve identical log file increasing (identical patch to the file) via doing something identical (probably it is going to fail because log files typically have some date on every line).

Then there is time to inspect the actual hardware.