Applied Math PhD Advisor dilemma I was hoping to get some opinions on my current situation involving leaving one advisor for another.

Background: I am a second year graduate student in applied mathematics and I have passed all my qualifying exams. In my first year, Distinguished Prof. K reached out to me and I began doing research with him. Prof. K is very well known in his sub-field of applied math. In the past year or so, Prof. K has helped me apply for two large fellowship awards (I don't know if I will get them or not yet) and we have met once a week for about 15-20 minutes. My concern is that when we are meeting, Prof. K doesn't doesn't help really at all on the math side of things and he is often distracted by emails/phone calls which interrupt our already short meetings. In short, he has become extremely difficult to work with and I don't feel like I have accomplished much mathematically.

Last semester, I took a class in numerical PDEs from a younger professor, Prof. N, at my university. I really loved the course and reached out to him about doing a research project last October. Prof. N is definitely one of the smartest people I have ever met. We meet once a week for a full hour and he is completely focused on helping me further the mathematics of the project. I asked Prof. N last week if he would be willing to be my advisor and he said he would be happy to. I cannot stress how much better the whole experience has been with Prof N. I really feel like he can help be really successful in my thesis.

A few notes: 
- Prof. N and Prof. K are in very different sub-fields of applied math. 
- Prof. K doesn't know about my work with Prof. N yet.
- Prof. N has offered to reach out to Prof. K for a joint project if I want.

At this point I am fairly certain that working with Prof. N would be better for me and my career. I really feel like I can be more successful with Prof. N in numerical analysis than I can be with Prof. K. I actually question a bit whether or not I could finish the PhD with Prof K at all because I receive almost no math guidance or help.  

Questions: 

1) Is the prestige of an advisor super important? Prof. N is definitely a much better advisor for me and, in my opinion, much better at mathematics than Prof. K but Prof N is not as far along in his career. I am wanting to make sure I can get a post doc position after I graduate without a super prestigious advisor.

2) Should I consider the joint project? My first instinct is that I definitely don't want to do that because I want to focus in the area of Prof. N and learn as much as I can from him. Prof K is just really difficult to work with and I am worried that joint collaboration with Prof K will just ruin the currently perfect project I have going with Prof. N. There is also some possible tension between Profs. K and N (all due to Prof K) that I am aware of and don't want to create a problem (I am not even sure if Prof. N is aware of this possible tension). I am sure they could both be professional if we were to collaborate though. 

3) I really feel that I need to tell Prof. K about my work with Prof N at this point and I am really struggling with how to do this. My first instinct is to do it in person; however, I struggle to finish thoughts in meetings because of interruptions by Prof K. Because of this, I was considering writing him an email and then talking in person if need be. Either way, I will of course be very grateful and professional in the way I do it. 

Thank you very much for your thoughts and input. Please let me know if you have any questions for me.
These things happen with grad students headed to one group deciding at last minute to go to another.  I wouldn't belabor it too much.  Be graceful, sure, but really I wouldn't even feel like you need to explain it or give K a pre-notification before you make your decision.  Same thing happens with job openings, house purchases, etc.  It's just part of life. K is a big wheel...you are a little new fish.  It won't kill him.  Minor annoyance but he will be on to emails and grant committees.  Of course figure out how to play it, but may even be better not to bring it up if you expect unpleasantness (the converse if you think discussion will mollify him.) 
Prestige matters, sure.  But being with someone you get along with is much more crucial (don't be miserable for years).  But if you are at a name department, it might not matter much...both are likely strong.  I would just make sure that N is not (1) unlikely to get tenure, (2) giving you too much of a sell job (some is fine, shows he cares...but just try to estimate how dynamic will change after advisor selection).
Personally, I discount handholding and apprenticeship.  Eventually you need to be independent.  But I am realizing math is a lot harder than experimental science in terms of making new work.  
I don't understand the use of the definite article "the" joint project. Is there already a proposal in play?  Or do you mean "a"?  

I actually might be mildly positive about a joint project in that you have your cake and eat it too...takes care of K with the fellowship letters...especially if you do get funded.  Plus having two bosses can be like having none.  You decide how to spend time with one or the other (gives you some power).  But of course you have to look at the specifics.  But if the "the" means something has already been floated, I might see that as a positive.  

Of course if K squawks at joint, then he just gets nothing.  But it is also true that if the joint thing is not working, you can probably even convert it to a solo with one or the other later.  Really I sort of love the option value here!
This is a little bit in contravention to (1), but I am capable of different ideas at same time:  perhaps there is a (gentle) way to play it so that both guys know you are in demand and drive some competition for you.  I inadvertently created this for myself during advisor selection long ago...this can be the case if funding is plush but students limited.