Sounds like you have the outline of a plan. I will qualify this now by saying I have done a lot of public speaking, but never had to do it in an interview setting, and not on this kind of topic so feel free to ignore me!! I have given lots of both informal talks and more formal lectures though.
In that type of scenario, I'd be tempted to have one slide per problem, with the problem clearly identified on it, and then just discuss your solution.
I would probably also start with a slide with a 'heading' of some description - the title of the job or something, as much to give you time to settle as anything, and have a small piece of opening blurb, again, to give yourself time to calm excess nerves (and by opening blurb, I mean something as basic as your name and a quick summary of the situation you have been given.)
Then a 'link' - as in, "The first problem I have identified is...." with a slide giving an outline of the problem (not loads of text, just a brief summary). Then discuss your solutions and reasons (I wouldn't necessarily have a slide with text detailing any of the solution - this is what you are telling them and you want them listening to you, but if there are diagrams that would help your explanation then you would need a separate slide showing these).
The other thing you can do is if you think there is a point that you haven't explained very well, check with them. Saying "Does that make sense?" is fine, and if people look a bit blank then it gives you a chance to go back and explain a different way. From their point of view, it means they have someone in front of them who wants to ensure the point has been clearly made, and who can read body language appropriately. If you fluff a sentence make a joke of it ("I'm sorry, I'll start that again and try and get a complete sentence out...") rather than stressing it's gone wrong and making yourself more nervous. People like a sense of humour, and it shows you won't be floored by a small thing going a bit wrong.
Try and make sure any notes you write yourself as prompts are easy to link with the slides, so if you forget that you were saying you don't spend ages hunting through pages of notes in small writing trying to find where you were. The prompts should have big big writing with the same text as on the slide, with the points you want to make smaller underneath (hope that makes sense!) so you can go straight to the right section if you lose what you were saying - quick glance at the slide, then quick glance through your notes for the same text...
Best of luck!