Speedsters are around, but as a certain web site says, they tend to change hands among the
cognoscenti before mere mortals catch wind of it. Try the 356 Registry web site
(www.356registry.org) and mailing list - interesting cars are posted there fairly often, I've found.
And if you're looking for a cheap alternative that takes advantage of the latest technology, I'd get a replica - eBay's crawling with them at bargain prices, certainly cheaper than building your own.
Btw, I'm pretty sure the Speedster debuted in '57, not '56.
Emanuel