I have to confess that I'm shocked that the 6000 hour FI with all that experience didn't have any contribution to make towards making this a safer flight.
The holes in the cheese were lining up and maybe you got lucky, but there were plenty of options to reduce the risks in the trip you describe. Most of which have been covered by other posts.
F214, and associated pre-flight planning - the route forced you to that level. Consider choosing a route that avoids icing, or at the very least affords you the option to avoid forecast icing conditions.
Four up in a C172 is tending towards the tricky end from a W&B perspective which may not help.
Once icing is recognised flying a non-FIKI approved aeroplane, you are now effectively flying an untested aeroplane. In the case of inadvertent entry into icing conditions, the POH calls for leaving by the safest and most expeditious route. Often this requires a descent to warmer air. In some cases the aircraft forces this because its performance is so degraded that it can no longer maintain altitude.
Use of flaps is often precluded in the case of icing. Your wing is no longer the aerofoil it was intended to be, and its behaviour is no longer certain. Changing its behaviour further by extending flaps is not a good idea, particularly when that same ice might prevent a retraction of the flaps. Knowing the POH in this case might have been useful.
Recognising that the tailplane will undoubtably also have been affected should have raised awareness that "feel" in pitch, trim management and speed control may also be affected.
The recommendation to wait further before landing to allow more ice to melt is good, if and only if the conditions allow it. If there was space, time, and fuel permitting it then handling checks and reduced icing could have helped.
Actually, it's great that you've posted this. I am sure that there are lots of people who hadn't thought about the symptoms, consequences and mitigations of this kind of risk. I am also sure that there are wiser people than I who can further add to and refine the advice regarding this scenario.