You are being very idiotic if you think Anderson is going to be ditched in the summer tests. He's been bowled into the ground over this year; so for the tests against Sri Lanka he'll get played if he is fit and in form. England's dumb move with Anderson was not resting him over one of the New Zealand series; which meant that he simply couldn't be fit for the Winter Ashes. Its a very similar story with Broad, and Bresnan is still recovering from injury, so shouldn't be ruled out. England's strength in the summer was the bowling attack; and as much as I think they need to try other bowlers (they need a spinner to back up Monty and for the future, and a few good seamers to come up); the core of the bowling attack IMO shouldn't be touched because at their peak, there is very little better in the world.
Batsmen-wise; Trott will be at 3 if he's recovered from his issues. It may not be a long-term thing; especially if its a similar thing to Trescothick; but he'll be there if he is ready too. There is much less stress in an late-spring home series against Sri Lanka compared to an away Ashes series. That solves the number 3 problem for now - its a question that should be asked, but I think that its not a huge issues.
Opening-wise; Carberry hasn't embarrassed himself, but apparently he's out for the fifth test anyway so that may be irrelivant. The way he played at the MCG seemed to be a "big score or you're gone" sort of innings anyway... Cook will open even if he is ditched as captain (which he should, that's been the weakest part of England's team BY FAR) - he's not the kind of guy that would throw his toys out of the pram after being sacked. Root should open IMO; he's young, and performed well enough in the summer Ashes to give him more chances. Carberry is good, but I think that they need to look for the future.
Trott should be at number 3 if he is able - but if not, they should move Bell up there if he can't. Keep Pieterson at 4 - he's often got out in dumb ways in the past, its just more noticible when no one else is scoring. I'd take him getting out in the 30s in silly ways for those innings where he scores big. Bell should go at 5 if Trott plays; with Ballance there as number 5 if needed.
Stokes needs to get another chance at 6 - I'm not sure of his abilities either side of the game, but he's definately been the best performing of the England players overall this series. In terms of the wicketkeeper, I'm not 100% sure about this; but they need to keep Prior in the loop; but also consider someone for now (Davies probably) and someone for the future (Buttler/Kieswetter? Both of those options depress me...)
Pace bowlers are where you are all wrong. Suggesting that an attack of Broad/Finn/Tremlett/Rankin would be good is a nonsense idea because the latter three are all very similar (tall, bang it in, not a great amount more). They need to give Rankin a shot (although part of me thinks that he became English just to allow Giles to have another overseas player for Warwickshire...); Finn is similar to MJ only much slower so he doesn't have the speed to be dominant. IMO; they need to get him back to his county and allow him to fix his action at that level (England can't do that stuff, look at Anderson). Tremlett is older, and much slower now so sadly probably isn't international level now. That leaves us with Anderson (who has a few years yet if England don't keep bowling him to the ground), Broad (similar really), Bresnan (rushed back from injury, but is useful at times in a Siddle-like way of being not very exciting but effective, plus also lengthens the tail if he's batting) and then someone like Onions (who really should have got a shot in Australia; because again he's something different). I'd go for something like Anderson/Broad/(Bresnan/Rankin depending on conditions)/Stokes for the pace attack; because its still the best thing that England has.
England needs a spinner in the team. Sure, he's not going to be as good as Swann, but its a useful thing to have to support the pace attack. Panesar is good enough for the short-term - look at India last year to show what he can do. It needs to be a guy picked for his bowling; so a Borthwick would need to greatly improve the bowling, especially since he hasn't bowled a lot at county level recently. Kerrigan is key - give him a few, low-pressure home tests against Sri Lanka, and we'd have a better idea what he can do without the pressure of an Ashes series; and let him build up to that. The captain needs to trust the spinner; and actually use them rather than go for Root all the time.
Captain-wise; Cook is too negative and too blah in the field to have a go; so they should move to someone else. Who that is, I don't know! Pieterson shouldn't be offered and wouldn't accept; which means that the future, appropriate long-term captains are really Bell and Broad (a few months ago you'd have said Trott, but not now...) You need someone who will actually control things in the field; and be assertive rather than what Cook is doing...
NOTE: I'm not 100% familiar with the county game outside of the games they show on Sky or what I hear; so I may be ignoring decent county players. I'd argue that's not a bad thing - look at all of the squads suggested for Australia before the series started that were Clarke + 10 random Sheffield Shield players; which would not have done as well as Australia did. You shouldn't chuck everything out; but you need a new, more positive captain and a completely new backroom setup (which means no Giles in a dream world).
First of all, I'm not sure you are right about Trott's illness being a short term problem. It sounds as though he has had it for a while. He may be able to play two pressure off tests against Sri Lanka, but what happens when England tour again? They surely can't risk him being part of a 16 man squad. It would just cause more chaos if he were to pull out again.
As for the openers, I agree with you that in an ideal world Root would just go back up and open like he did with moderate success during the summer. However I am just starting to think that perhaps he needs to get away from it for a while. We've mucked him about in terms of batting positions, and we'd be moving him again if he were to open in the first test against Sri Lanka. I wonder if it would be more beneficial to tell Root that he will be back opening soon, and let Compton have the summer in that position. It definitely cannot be Carberry. He is 100% not good enough.
I think Bell should move up to 3 to stop our run rate getting stuck in the first 30 overs. I'd also bring Ballance in for the same reason. That leaves the KP dilemma. Do you dump him like a lot of people seem to want to do? Or do you stick with him and accept his madness? I was in the first camp just a few days ago having seen the way he got out against Johnson in Melbourne, but having thought about it for while, I think that this may be the right time to give him the captaincy back. From memory, he was quite forward thinking tactically, and it was just a row that ended his time in charge. Probably won't happen though as long as Flower is coach.
Stokes needs a whole year as allrounder before we can decide how much benefit he adds to the side. So like you, I'd leave him at 6. I also agree that Prior needs to be kept in the mix for a while. The break he is having now and will get once the one dayers start might just be all he needed. Buttler is a superstar though. I'm sure of it.
Don't agree fully with your assessment on Anderson. England use this term 'the red zone' to describe an amount of cricket that is too much for the body to cope with. They monitor it carefully, so Anderson wouldn't have gone into it. They have rested him during ODI series'. However I do agree that in recent test matches he hasn't been getting the necessarry rest period during the 5 days of play, as the batters have let him down. Consequently, his performances have dipped. I'd keep for now, but I don't think his bowling is getting any better. Worrying sign when he doesn't swing it in the opening 10 overs. Even with a kookaburra ball. For me the attack will be Anderson/Broad/Bresnan and Finn. No spinner I'm afraid. Nobody good enough, unless someone can convince Kerrigan that The Oval was a one off, and he is now the best spinner in the country now that Swann has retired. It sure as hell isn't Panesar. He's been useless for a while, and I think the England management have just started to realise it given the way they treated him during the 4th test.