GouldieFledge
The birds can be transported in a smaller cage.
As to the flight.... hmm. If you could find someone with a pickup truck. You can stand it towards the back , close to the tailgate, then lay it gently backwards toward the cab of the truck. Tuck old blankets, towels, pillows (what ever you have) under the part that's sticking up, to give it support. Then bungee the whole darn thing to the sides of the truck. It will travel beautifully.
The only reason I know it works.... I moved recentry as well.
Had to drag several large flights, cages, 80+ birds, fish tank, fish, two dogs, etc. etc. The F030's, had to be disassembled and reassembled, they didn't fit well in my son's smallish truck.
Hope you manage somehow.