Well, it may not be even close to the method desired here (making log entries while in the game) but, a realistic method already exists in SH3 Commander..."Review Patrol Logs" permits the user to add/edit log entries after completing a patrol.
I wrote "realistic method" because that is just like the old-time process for producing the USN Deck Log, or "Journal" or "Diary" as it's called in other services. A "rough" Log (the Quartermaster's Notebook) was kept on the bridge (surface ships), or in the control room (subs), where the QMOW (Quartermaster of the Watch) made hand-written entries of the ship's navigational data (position, course, speed, changes in course and speed, etc., etc.), weather observations and all the significant events taking place in/on and around the ship. The information in the Notebook was later transcribed into a type-written "smooth" Log (as well as being used to produce Patrol Reports and such); affording the CO an opportunity to add details and "smooth" the information (fix errors...the rough Log and smooth Log were both turned in to the Bureau of Navigation, later BuPers, and any discrepancies would be thoroughly investigated (been there, done that!).
Maybe it's just a force of habit, but I find it convenient and very "realistic" to keep notes...a "Rough Log"...while in the game and then transform those into "Smooth Log" entries after returning from patrol. Of course, if you don't use SH3 Commander, then it can't be done this way.
Nonetheless, I do hope one of those wonderful "hardcode guys" can find the fix you're looking for; it would be very handy.

I presume it would also produce a Log that could still be edited after-the-fact in SH3 Commander...?