[A Goofy Family]

Treat this trip as a "trip of a lifetime"...that's what we did when we took our kids in 1999 for their 5th birthday, but now we have 7 trips under our belt and 2 more planned for this year!! It's addictive and somehow we find a way to figure out another trip. As recommended above, get with one of the Mousebuzzers that have DVC points to rent...it's a really great way to go and you get a mini-kitchen in a studio and a full in all of the others. We are DVC owners, but our friends that do alot of our trips with us have found it to be very easy to rent points and stay at the resort with us. Works great!
As for your concern for your little ones missing out on their birthday celebration, here's what we did when my sister & I went a few years ago with our families. We went in March. DNiece's bday is in Feb and my twins are in April...DNephew's is in October. Since we were going at a half way point between the twins and Dniece's..we celebrated their birthdays, but we celebrated Dnephew's 1/2 birthday...no questions, just lots of birthday wishes and all the kids had fun together, no one felt left out.
Our 1st trip was in April too, so I'm sure you'll love going then...great weather and crowds are good too. Sounds like you have a good grasp on planning costs and budget. Keep us posted and let us know if we can help!