If the author of "plod" might object to having his/her code posted here, that's understandable. If you're able to alter your copy of "plod", you might consider adding the functionality that you want -- it would be pretty simple (if the code is already reasonably well written).

If "plod" has a file handle for the log file, and can use the "print" command on that handle, you just need to add a new single-character "plod" command to print the current command line string to the log file (and then pass it to the system call as well).

For that matter, if "plod" does not provide its own "history" functionality, I'm surprised that you find it useful, and I'd expect that this is the next bit of functionality you'd want to add -- an array where you push each shell command as you execute it, and (this is the slightly heavy part) some tilde command keys to list the array, search for strings in it, save it to a file, etc.