Heiki roof light fly screen cleaning

Our 15 year old van has seen 80 - 90 days use per year. The Heiki roof flyscreen is now looking grubby and a bit “clogged up”

I’ve tried cleaning with a minimum amount of soapy water but this did not get into the corners and so it now looks worse!

Has anyone successfully cleaned the flyscreen? Which product did they use? How did they prevent the blind becoming “floppy” and loosing its folds?

Any suggestions would be appreciated.