Saw this thread and I just had to reply !
Household cleaning agents are a definite "No No", as they contain solvents which attack the surface of visors. It causes microscopic cracks in the surface of the visor causing a visible haze (if used over time), but worse still, causes an inherrent weakness in the visor, so if hit by a stone, it can just splinter and shatter.
I used to import a "non-solvent based" cleaning and polishing product a few years' back from the US, specifically for plastics (It was used by the USAAF for cleaning the cockpit canopies on their fighter jets). A brilliant bit of kit, but the cost was prohibitive (although a bottle of the stuff lasted at least a year, it was difficult to see the value of ?13.95 in a relatively small package - this was the retail cost to my customers).
So, I recommend soaking a kitchen towel in warm water, laying it over the surface of the visor for a few minutes, and the dead bugs just wipe off. For a good clean, use a vinegar based clear glass cleaner.
Before I got wise to this, I had an Arai visor shatter - I too had been using Mr Sheen.