We have a seed exchange in Jacksonville.
I don't know if what you want is available, but you can always ask for it to be put on the wish list:
About « Jacksonville Seed Exchange
You can also give a call to Flying Dragon. I was there recently and noticed they had a good-sized collection of coonties (zamia), which is not always such an easy find. Palm seeds would probably be a special request, but they might be able to do it, they're a real mom & pop place:
Flying Dragon Citrus Nursery (broken link)
Let me know how it goes! I'm curious to see where you end up finding your palm seeds
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