About 8 or 9 years ago I spent a lot of time trying different methods of reducing noise in the cockpit by fitting insulation. See
https://www.sonexaus.org.au/galleries/building-tips/cockpit-noise/ on the Sonex Australia site for more details. Unfortunately the article I wrote has lost some of it's formatting making it difficult to interpret the data so to summarise, nothing worked very well. I could get some noise reduction at low RPM and high RPM but hardly any useful effect at cruise speed. I think a muffler on the engine would help (Jab 3300) but there is barely enough space in the cowl to fit one. At present I have the oil cooler fitted where the muffler would normally fit on the Jabiru engine. If I could fit the muffler in that location I think it would have to be heavily modified to fit inside the cowl.
Peter