Thank you all for the help!
I think we have found the issue. The mechanic removed the plugs, and said they were some of the worst-fouled plugs he has ever seen, which is surprising since it had its annual from the same place late October. We did have fine wire plugs put in at that time, and have been putting Alcor TCP fuel treatment in the fuel ever since (because of previous fouling issues). There was also a bolt missing from the exhaust stack that was replaced; they indicated that this could have caused more air to be sucked in and contributed to the problem. The plugs were cleaned, the missing bolt replaced, and the engine is running great. Mag drops on both right and left are dropping 80 rpm (what it was before).
The problem came on suddenly after I had been doing practice ILS approaches with my instructor. Very little time in between approaches to do any leaning, and the fuel pump was on quite a bit. This surely could have contributed to the problem, but the main problem seems to be too much fuel on a cold start. I was following the standard checklist procedure: fuel pump on, throttle one turn, mixture rich 3 seconds, mixture lean, fuel pump off, and crank. I was told that this engine is easily flooded on cold starts, and that I should use the following procedure for a cold start: fuel pump off, mixture full rich, one turn on the throttle, and crank. If it does not start, turn on fuel pump for 1-2 seconds, and crank again.
I will update again after a few more hours of flying time. See attached photo. This came out of the spark plugs (both top and bottom). Don't worry, the pocket knife didn't come out of the spark plugs (just for size reference)!