The only way for you to do everything you want would be to add you to the entire reservation. Though this would add the extra-adult charges for nights you aren't there, but that's the only way to get you onto a package reservation that would give you all the same features of that package, including Free Dining if your friends are booked under that.
Arranging DME transportation would work fine, even if you're not arriving or departing on the same day as everyone else. But I'd suggest talkingw ith DME directly (866-599-0951) to arrange things, as Disney Central Reservations sometimes has problems getting the "out of the ordinary flight itineraries" into the system.
You'd also be stuck with whatever ticket option your friends had already booked under the package. If it's still outside the 45-day window (and it just barely might) they can call, lower *all* the tickets to what *you* need, and then after they check in they can individually upgrade their own tickets to what they need for their week-long visit. (They'll end up paying the same price for the tickets in the end, but some will get paid up-front, and the balance will get paid when they upgrade the tickets)
One side-effect (benefit?) to this plan would be that you'd have extra dining credits. If they're there for 7 nights, and you're only there for 3, there are 4 "unclaimed" sets of credits for the nights that you *won't* be there... You and your friends would have to work out between you waht happens to those credits... (Do you splurge and upgrade one meal for all three of you to a Signature? Do some of the Quick Service credits get used for breakfast?)
Apart from all that, your friends *could* add you as an extra adult after they've checked in, and it would only be for the nights you'd actually be there. But doing this you would *not* get the tickets or dining plan features of their reservation. It would be for the room only. (It *might* also get you DME transportation, though I'm not 100% on that one)
-Rob
