Is that the Louisiana Palmetto? I'm not too familiar with the palms. That sounds like a great idea though. How nice it would be to have palms in the forests and wooded areas instead of escaped colonies of Bradford Pears and other undesirable non-natives. I've been looking closely at the seeds of different palms and other more tropical but yet hardier types of tropical plant seeds for sale. I doubt that I'd have much luck here, but I have family in more southerly states where I think the hardier tropical plants would have a chance at survival (such as Windmill Palm, Louisiana Palmetto, Joshua Tree, Silver Mazari Palm and more zone 7 and 8 or so selections).
But back on spreading seeds around the area, I've thought about going around like the man in the story and dropping acorns in a hole made by a cane or other stick, of different trees (maybe Bur and White Oak for example) to bring back real forests of yester-year. I have taken plastic bags of seeds with me on walks and sprinkled them around before. I've even wrapped American Sycamore seeds in toilet paper and a rock and threw it into a muddy creek-bed in my friend's backyard. One of these days I'll look back there and see if any grew, that was several years ago, so they've had time to grow.
Will

I am also trying to get live oaks growing here too, but I will probably be dead by the time they reach a nice size. I am going to sow some Sabal Minor in the woods in a couple of weeks. Sabal Louisiana is a variety of Sabal Minor or otherwise known as the Dwarf Palmetto as it rarely gets any significant trunk to it.

Fertilize those live oaks every month and make sure they don't get dry and they will grow much faster.

I will give them a bit more fertilzer this year to see if that helps them grow a little more. I was looking at the palms today and they all are looking great even the smaller ones planted from seed. I can't wait until Spring gets here!

Although im not responsible for naturalizing them myself, Washingtonia robusta, Washingtonia Filfera and Phoenix Canariensis have escaped cultivation and have naturalized throughout central and southern Cal. Robustas are native of Baja California (Mexico), Filferas are native of South Eastern California and the Phoenix are from the canary islands. I have to admit, there is a drainage basin less than 30 feet from my backyard and i have thought about planting caryota urens in there. It is always wet there and evenly moist throughout the summer so i wouldn't have to worry about watering it, and i would be able to see them from my yard.

Well the birds have already been doing it for years i'm sure they'll help ya spread em out.

Yes, I'm sure when the Sabal Minors set fruit in a few years that they will be very attractive to birds who will disperse them naturally. Too bad Sabal Minor was erradicated from Virginia either early in the Colonial Period to the plow and cattle or during the last ice age as it would be nice to see them growing around here naturally with some size.