I'd be interested to know what the problem is flying in the vicinity of a cyclone.
Throughout Ingrid I was at Airlie Beach, checking the BOM site to see if Mrs Claret and our unit would be there when I got back, so I don't have any empirical experience of it.
However, in the past I've flown past/abeam cyclones. Invariably the Wx forecast has been something to the effect of "clockwise flow to 100 kts, within 100nm of cyclone centre". On all occasions the flight has been as smooth as silk, though the ground speed may not have been anything to brag about.
I have a work colleague who flew into the eye of a cyclone years ago in a bug-smasher, not believing the poor ground speed he was indicating. As best I can recall the flight was smooth enough, just slow.
This begs the question, what's wrong with flying in the vicinity of a cyclone? Prudence, and probably the TAF, would suggest an alternate should be carried. After that .....