I have a chance to buy a trunklid from New Mexico (Albuquerque) and am wondering the best and most reasonable way to ship that? Destination La Crosse, WI., or anywhere in Midwest.

Greyhound is frequently suggested for this kind of stuff. Cheap. It just gets thrown in the bottom of the bus w the rest of the luggage.

If it's the 70 RR Decklid I saw in the WIW. I would have it wrapped in Carboard sheets and taped up. It's an easy shape to do it with. I bought one from Texas for my 68 Coronet and it arrived perfect Via Grey Hound Bus.

remember when you ship ANYTHING it needs to be able to survive a 8' drop. Pay the seller to pack it extra well and take pictures of the box when they deliver it to the depot. )double box and foam) cheapest is not the best option here. fastest is. The faster it gets to you (theoretically) the less chance it will have to get smash or driven over.
i have had good luck with ups shipping sheet metal. ......amazingly

how your stuff gets handled

Wood crate for me.

I bought a fender that was shipped greyhound and it showed up with a nice dent in it.

I've had trunk lids and doors and fenders shipped with Greyhound and never had a problem. They are the cheapest by far. Think about it, how many people actually ride the bus with lots of luggage. Those busses run all over the country with empty cargo holds. The longest I ever waited was 4 days for a 48 Dodge trunk lid from Oregon to Southeast Missouri and the cost was under $100. That was about 6 years ago. Wrap it in cardboard with bubble wrap and duct tape and you won't be disappointed.

if a guy goes to a local body shop, often times you can get the boxes new, late model, hoods, doors, and gates come in.
they make perfect "starter kits" for packing up sheet metal.
also, look at windshield boxes. sometimes they work as well.

1x3 furring strips with cardboard stapled to the inside is the ticket

your best bet is visit a VW body shop. ALL body panes are shipped in sturdy cardboard boxes. including entire sides of a car, this is the only way you can buy a 1/4 panel on some models. we get boxes 20 FEET long by 1 foot wide by 5 feet tall on a daily basis. fenders and hoods are in good boxes also. if you get a VW body part damaged in shipment it was probably damaged before it wen into the box.