Hi Pan, and welcome
Hope we can help you out here.
As you can see, I am in Florida, so my soil and climate are somewhat different than yours, but I have a couple of thoughts to offer: First one is that you said there was a huge dogwood tree crushed by one of the falling pines, right? So you absolutely know that dogwood will succeed in your yard. If it looks like a good place, I'd try planting another dogwood or two right where that old one was. You might have to chop out the stump and dig up some old roots, though.
You also know for sure that the pines and oak will succeed. Are you absolutely sure you want to struggle to grow ginkgo and eucalyptus? I've only seen them growing in drier climates like California and Utah where we used to live - don't know if they are good for Louisiana. Just because the tag says a tree will be "hardy in zone 8" doesn't mean it's going to be a good choice. The zone hardiness just tells you it will survive the average low winter temperatures you get. I'd recommend you walk the neighborhood and see what other trees are doing well close to you. They might be better suited to the heavy soil and humidity your yard has to offer.
Another word to the wise - just because you see those trees for sale at a garden center also does not mean they are a good choice. Places like Home Depot, Lowe's and Wal-Mart get shipped a lot of plants that are not suitable and should never be sold where the store is. They probably ship the same stuff to stores in Tenessee and North Carolina. Go to a good nursery and talk to someone who knows trees.
The other thing to watch out for is planting your trees so eventually they will grow up and shade your butterfly plants (which for the most part need sun to bloom). So you don't want to plant any trees too close to the south side of the butterfly garden, or too close in general, because a tree will spread its roots even further than its branches reach, and could eventually compete for water and nutrients with the butterfly garden. Make a plan and plant trees strategically so they will shade where you want them to, and also of course, not be too close to your house that they could eventually pose a danger when another hurricane happens along. You can't depend upon being lucky twice, right?
@RickCorey is our resident expert on amending heavy clay soil so I hope he will bring you some words of wisdom.
