Do you have a general OBDII scan tool that can read\display live data & Mode 6 recorded engine component test data? I ask due to me interpreting from your posting that you appear to not have 1. If you don't I would highly suggest you get 1 that can give you all this data so that it can assist you w\ diagnosis...………… A good, relatively cheap 1 I would recommend to get that has a good screen viewing quality, can read\erase DTC codes, graph\record\playback live data PID's, do IM readiness (emissions) data & give you access to the PCM's stored engine component test results (such as the engine misfire monitor data recorded during cold starts as well as normal operation which can give you a window into what you're trying to figure out concerning misfires for starters) is the Foxwell NT301 OBDII scan tool. From Amazon for $65.95 + tax & needs no internal battery as all powers up from the OBDII port. Foxwell also makes a nice storage case for this scan tool but it is a separate item & not included w\ the tool.....
If all this is new to you then I would suggest to read the tool's instruction booklet to familiarize yourself w\ it's operation & usage & if you know of a buddy close by that has experience reading\using 1 of these to assist you in using it to interpret the live data & stored data readouts to help to diagnose you car's symptoms...…. Also if you have access to YouTube you can access the myriad of videos of folks explaining these systems & demonstrating TS techniques to locate, interpret the data to ID the source causing issue. Put focus on the videos put out by actual ASME trained auto technicians (there are quite a few of them out there)…………….. Just type in the search bar the topic of what you want to look at...……..
What you want to be looking for in addition to Mode 6 data is the actual operating STFT%\LTFT% fuel numbers (especially focus on the LTFT% numbers 1st but don't disregard the STFT% numbers either) along w\ MAF readings at engine idle, low RPM's as from my experience these 3V's are fairly sensitive to rich fuel readings (seeing the LTFT% number being a negative number...example: B1 LTFT @ -5.7%, B2 LTFT @ -9.2% at hot idle....an indication of excessive fuel injected during OL cold start then w\ PCM reaching CL operation it readjusts injector pulse time to cut fuel back according to MAF reading which can cause engine misfires due to heavy fuel wetting the spark plug tips until engine operating temps heat up enough to help the heavy fuel atomize better then the misfires may stop. Misfires can be fuel related as well as component related (coils, plugs, etc), either wet (rich) or dry (lean) but these 3V engines are actually designed & tuned by Ford to run in some low level lean fuel conditions thus are typically more sensitive to over rich conditions vs over lean conditions at lower RPM's (emissions & MPG concerns) when misfiring is encountered (using the OEM tune...if remote or dyno tuned then will be according to what the tuner was trying to accomplish). The amount of misfires recorded has to reach a very high number (>65,000 recorded misfires per engine cylinder) for the PCM to turn on the MIL light so yes, you can have these happening but the MIL doesn't light up as this monitor resets itself on every drive cycle (when the car is shut down & ECT drops below a certain temp over a certain period of time that tells the PCM to run a new component test drive cycle). This is why the Mode 6 data is important to read as the PCM records\saves all this data history for technician diagnostic purposes.
If you really want to figure out what's happening w\ these S197's you need to have on hand at the minimum 1 of these general OBDII scan tools to get access to the PCM's live & recorded engine component data & some system operational training of how all this works to be able to effectively diagnose\repair issues w\o being a parts chaser just throwing parts at every assumed cause until you may get lucky & change the right part......saving you money, time & headache in the process.
Hope this helps.