Stunning co-incidence, I'm having the same thoughts. Have dedicated an old and dying laptop computer to Radio 2, hooked it to the home network and wired it to the Hi-Fi - and use it just to listen to BBC Radio in Florida, especially the "Listen Again" feature already mentioned.
Going one step further, if we manage to save material through Total recorder or whatever I can find as this thread runs its course, would it then be possible to record onto CD-RW's to play them in the car, or airliner, whilst travelling? Would a flash drive MP3 type thing be better?