If you do it yourself just make sure that the cages are covered to keep them from jumping up and hurting themselves. Perhaps a dark box van or enclosed trailer during the cold part of the year so they don't overheat.
That's good advice! I moved mine about half that far and carried them in very large, wire dog crates, two birds to a crate. I put bird buddies together to prevent fighting. I covered the crates with towels & blankets to darken them, and the birds did even better after it got dark outside. Birds jumping up in the crates and hurting themselves is a real concern, and even when the crate is small, a panicked pea will explode up into whatever space it has, and bang itself into the top of the container, at least mine did & do.... I also put towels and bedding on the bottoms of the crates so that the birds had better footing, which helps them not be so anxious. And of course, drive as sedately as possible, because cornering and abrupt maneuvering also makes the birds fearful and increases the level of agitation.
It's obviously easier to move males when the trains have dropped, but not always possible. I've seen photos of birds with their toails wrapped for shipping, but I haven't tried that... maybe someone who has done it could post an explanation or some photos?
Assume the birds will get loose stools from the stress, and make sure to have electrolyte solution for them on the far end. I would probably try to travel at night and not open crates in the middle of the trip to avoid disasters.
If you are going to be making multiple trips back and forth, perhaps you can take a smaller number of birds on each trip, perhaps in the passenger compartment of your vehicle? Obviously you can't leave birds in a hot car, or a hot trailer, or a hot U-Haul van... even for long enough to have lunch! An advantage to having the birds in the passenger compartment is that you know how hot/cold it is and you can monitor how they are doing. But it may not be feasible if you are only making one trip and need to move all those birds at once. So as @KsKingBee suggested, moving during a cooler time of the year would be safest.
I really want to hear how you are going to manage pens for 40+ birds, 500 miles away -- wow, I'm impressed at that!