Thanks Robert.  A month ago I finally learnt how to use the Lirc-mouse after several months struggling.  Now I use it to navigate the iPlayer (in Windows I similarly use the FirefoxIntegrator, a MediaPortal plugin), but I could not handle the sound with the Lirc-mouse.  The Windows commands type {app(0x80000)} don't work with the Flash player as such, but apparently work directly with the audio hardware - I believe that is the term I have seen used.  Anyway it works for me, and now in Linux the pulseaudio-module-lirc solved the problem.  Also this seems to bypass the Flash player and directly control the audio mixer.
Believe the tab-navigation is with the browser and not with the Flashplayer.
I was not aware of the Bigscreen version - seems great!  Have just tested it for five minutes, but believe there is a problem how to get out of the fullscreen video as the remote escape command does not seem to work, nor receiving any other keyboard shortcut.  The audio commands still work though.  Had another go just before sending this off and found that Alt-F4 works to exit the fullscreen video.