Thanks to everyone for the informative and humorous responses!
Ron H: Thanks. All of the boxes that we are putting in checked bags are models in the oringal manufacturer's shipping boxes. So in the case of the Atlas items, the models are snugly fitted in styrofoam within the OEM boxes, and then teh OEM boxes are in a cardboard box. In the case of Sunset Models/3rd Rail, there is even styrofoam between the outside of the OEM box and the inside of the cardboard shipping box. Also the plan is to stop by a Staples (or other similar store) and buy a large roll of bubble wrap (or packing peanuts).
gunny: Thanks for the idea. I'll contact FedEx tomorrow.
Jan: Yes, they pulled my carry-on to the side when I came back from Reno last month with several Atlas SW-9s.
mwb: I have yet to lose any baggage during travel. Of course I'm hoping you are wrong. After all, if they were shipped Priority Mail (which would be insanely expensive) they would still be thrown on a plane.
Volphin: Thanks for the breath of fresh air!
Nation Wide Lines: Planning on 3 hours to Stout (map says more like 2 1/2 hours), then 2 hours to Mr. Muffin (map says 1 1/2 hours), then 3 hours back to MDW (map says 3 hours). So 6-7 hours of driving, plus the time we spend at each stop. And I'm not too worried about them opening the cardboard shipping boxes, as long as they don't damage the OEM boxes.
MikeH: Only way I could have avoided the taxes was with a reseller's tax ID number. Working on that now for next time!
Arthur: You ain't kidding! I didn't put in any live bids. I went through the auction and put what I thought were very conservative bids on several items that were of interest. The only item I REALLY wanted (like I was prepared to increase my bid during live bidding) was the Sunset 3751. But then as the auctions came rolling through, I was like "dang, that bid won? Oh, and that bid won? Wow!"
bob2: One of the auction lots I won was a 10-car set of Super Chief (1952-53) aluminum cars by Golden Gate Depot. I currently have an order with Golden Gate depot for the 1938 set, and they are charging $160 for shipping, and we are both in California! So even if that was all I won, I'd be paying $90 in airfare (plus rental) instead of $160 shipping. And the risk of transmission on planes is way lower than going to the grocery store or post office.
Trainchief: Thanks for the good news!
FlyPlanes-PlayTrains: Not too worried about the cold waiting to be loaded, but prospect of being "submerged in glycol" is a bit horrifying. Doesn't seem like doing that to customer's bags on a regular basis would be good for business. My heaviest bag will still be under 30 pounds, and the Southwest weight limit is 50 pounds per bag. So no extra charges there. I think about 30 cubic feet total, too much for the closet.
MikeinTallahasse: We did all carry-on for our recent trip to Reno. The one item not in OEM packing and the 4 items not in shipping boxes will be carry-on.
Simon Winter: I thought the 3rd Rail item was packed great, well-wrapped in paper and plastic, then taped to the wood board, just like it would have been coming from 3rd Rail. But the drop on the end was still enough for the draw-bar to poke through the box and bend on my cement porch. But my thought was that any shipping method they are getting tossed around from container to truck to another truck and so on. I have been in line many times at the US Post Office, watched a customer come in and set pre-paid packages on the counter, only to see the clerk toss said package 6 feet into a bin with other packages.