Applied Math PhD Advisor dilemma
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.