Due to the 12 year age difference between our kids, we always invite one oldest DS's friends to go along. The only thing we have ever asked is that the friend have their own spending money. We pay for everything else.
We look at it as part of our overall vacation expense and our son has a great vacation (not hanging 24/7 with people that don't know anything

) as well as the rest of us.
As for asking the other parent to pay, here our my thoughts
As a PP already stated the room and limo costs do not change therefore the other parents should not be asked to offset them.
The only additonal cost that is added to your trip for this extra person is
1. spending money
2. dining plan
3. park ticket with hopper
4. plane ticket
Spending money - I do not think anyone would argue with you asking the parents to send money for souvenirs, extra snacks, games, etc. for their child. Let the parents decide what amount they want their child to have, only they know what they can and cannot afford to give them. The parents can either give it to the child in one lump sum and when it is gone it is gone or they can give you the total amount and each day you give the child a certain amount. Any additional shows, misc extras, etc that were not pre- planned should be paid by you.
Dining Plan - Our family do not use the dining plan. No way would I want to pay for the Deluxe Dining Plan when I know that I could spend way less doing counter service and packing snacks. Our kids could care less about fancy meals it is all about the parks and characters. You want the signature restaurants, therefore you should foot the bill.
Park Ticket - Cost is the cost. We are fans of the park hopper option. I as a parent would be okay paying this.
Plane ticket - Kinda tricky on this one. I search around for the best deal on airfare before I book flights for our family. What I consider a good deal and what others have paid and thought was a good deal are 2 entirely different things. I would have a problem just letting someone book it and having to be stuck paying that price. Maybe print out a few different airline prices. Find the average price (including luggage fees) Give this price to the parents as the maximum price. If booked cheaper they would only have to pay that cheaper price, if booked at a more expensive price you pay the difference. I as a parent would be okay paying for this.
Using the above you would be asking the parents to pay for airfare $400 (your estimate) 5 day park hopper $280 wo/tax, and spending money $100 (estimate) Total for 5 day vacation approximatey $780.00
For some this would be great deal, for other it would be a budget buster (as one PP stated she is going on a 10 day vacation for $1500 less than what you are paying for a 5 day)
Me personally, it would be hard to justify spending that amount of money for a vacation for one member of the family unless it was used as their xmas gift (which would also mean grandma would be getting them a gift card for their spending money, thus less overall cost to me) .
I will also admit that in my thinking I am having a hard time with this just being a 5 day vacation , why not 7 or 9? Airfare is going to be basically the same amount. Park tickets only increase $6 each for a 7 day or $12 each for a 9 day over the price of a 5 day. With taking that into consideration I would be more respective to paying the $780 for a 7 or 9 day vacation versus the 5.
Adding -
In this economy and not knowing the other families financial situation, I would have a hard time asking them to pay approx. $800 for a vacation.
If you can not afford to pay the entire amount (except for the spending money) and keep your fingers crossed that the other family offers to pay something, I would not ask the parents if they child could go.