Have any of you ever moved residences with your birds?
Yes, multiple times - moved out of my parents' house into an apartment with a roommate; out of the apartment into a rented home after getting married; out of the rented house into our own house; out of that house into our current house.
What was their reaction?
I've always taken my birds out and about with me. I've frequently moved my birds cages around the room/house. I have spare cages all over the place and I play musical cages whenever the urge hits me. I don't really do the schedule thing except for making sure they get plenty of sleep at night. So my birds settle in after a move really easily. This includes an african grey which I was told would not take to change well at all. She was fine.
Have any of you ever driven cross-country with your birds?
No, but I've RV'd for weeks at a time. See my thread that I started:
viewtopic.php?f=7&t=5256How did you house your birds for the drive?
Small, tiny carriers just barely large enough to turn around in but could hold food and water. I got some cheapy, larger cages that collapsed so I could put those together really fast for temporary housing when we got where we would be staying overnight.
How did the birds react to being confined for that long?
The birds got out of the tiny carriers several times a day to stretch when we'd stop for food, bathroom, scenery, etc. So they didn't really seem to mind being in the tiny carriers. With all the other excitement they'd use carrier time to eat, drink, nap.
Your budgies that aren't tame, maybe do the collapsible flight cage and have it on top of your car. That's going to need a bit of a logistical planning since you can't really take them in and out of the flight cage several times a day. I think they'll be ok waiting until evening when you guys stop for overnight to get into the flight cage (or let them fly around the hotel room and just clean up after them).
You can train them to fly into the flight cage without you having to physically catch them up. That might be less stressful for them. I discovered this with my first finches. I'd set them loose to fly around my room when I was cleaning their cage. After cleaning and putting fresh food and water in I'd be chasing them around the room trying to catch them to put them away. The door to the cage was open and since the cage is their known safe place, after a while they started flying into it.
Then I kept doing what I was doing - letting them fly around, cleaning cage, chase them around but instead of catching them, I'd whistle as soon as I saw them pass the threshold of the cage door into the cage. It didn't take very long for them to connect the whistle with going into the cage and I could just whistle and they'd go into the cage. I think to them it beat being chased around and caught up.