My suggestions would include extending the world news simulcast on BBC One and BBC News in the early mornings until between 06:30 and 07:00 as the amounts of viewers awake at these times is no greater than late in the evening which is already simulcast and additionally because WN is already focused on Europe at this time of day. As this would allow breakfast to start later I would either extend it on BBC One and the NC to 10:00 in order to cut the daytime budget or finish it at 09:00 on BBC One so that the Salford team can continue on the NC until 10:00. I would also reduce Newsnight to be broadcast for 30 minutes and on Mondays-Wednesday's only (as the viewer base is watching question time on Thursdays and the programme tends to be light on content on Friday's in any case).
Another possibility would be to simulcast politics live on the NC and get the morning NC presenter to also present the One (which is no different to a typical NC half hour except for an in studio weather forecast) so that one presenter can cover from 10:00-14:00. Furthermore I would scrap the Five and extend Afternoon Live until 6 or simulcast with World between 17:00 and 18:00.
I would also scrap the need for a sports presenter on weekdays with any important stories being covered by the main presenter and the less important ones being dropped (there is no need for 3 reports back to back on the Australian open for example) but maintain a business presenter in a similar role to a present.
At weekends simulcast with world until 08:00 and then have a single headed version of breakfast from Salford until 10:00 on BBC One and 12:00 on the NC on a Saturday and scrap breakfast completely on Sunday with the extra hour absorbed into the London NC rota. I would also drop the Saturday edition of PM and make the Saturday version of Today and weekend breakfast on 5 Live single headed.
On radio I would turn 5 live into an opt of world service with only its own breakfast and drives shows (and any sports opts needed) and also simulcast this with radio 4 and local radio overnight. I would combine the news bulletins on radio 2, radio 3 and radio 6 music and also on radio 1 and 1 extra during evenings and weekends, but would maintain Newsbeat during weekday daytimes.
Outside of News I would close the linear red button and BBC Scotland in their entirety, would reduce some sports coverage noticeably giving up Wimbledon as producing coverage of 15 courts some of which are watched by a handful of people at best is not even close to a good use of resources. I would merge BBC 4 into BBC 2, would create a distinct strand for BBC3 on BBC2 between 22:00 and midnight on Thursdays and Fridays, reduce the numbers of programmes in genres well covered elsewhere such as period dramas and weight loss documentaries. I would also make 6 Music a part time station so that it only broadcasts between 7am and 7pm Monday-Friday and 9am-5pm at weekends, would close down all AM radio frequencies outside of rural areas that cannot recieve a FM or DAB signal.
Wow, where to start with this mess! Firstly Radio 1 and 1xtra already share news 7 days a week, and don't have many updates after 5.45 Newsbeat during the week anyway, so there's no savings there. Apart from weekday breakfast on Radio 2, the same presenter does Radio 2 and 6 Music news, one on the hour, one on the half hour, so no saving there.
Why does 6 Music have to be reduced to those silly times? Why not Radio 3? Or Radio 2? Is that because you're not a listener of 6 Music?
The first half hour of weekday Breakfast is in my opinion the most news focused of the whole show, handling the developing overnight stories, newspaper reviews, sport, weather and local news. I take it, you're not up before 7, unlike so many viewers?
While i agree that something needs to be done about the content on 5 live, your idea of being an opt out service from the World service doesn't work. If you are going to cut it down so much, just close it!
I'm also getting the feeling that you aren't a tennis fan, mentioning the Australian Open and pointless Wimbledon coverage, but Wimbledon is one of the BBC's crown jewels.