Like you, I had tracked my flights via a compiled list and, yet, was stuck on progress. I had a similar issue with the Greased achievement, so just decided I’d re-fly every landing challenge and aircraft 300 miles again and see if that would result in progress. It did, and I was very surprised to find that aircraft I’d noted as counting towards progress counted as progress again, once I re-flew them.
I completed both on 5/5.
The key to success (based on information from another thread here on the forum) for Jack of All Planes is ensuring you take off and land at towered airports after obtaining ATC clearance.