With waney edge boards you generally pay a premium for width, above about 400mm wide they become progressively rarer and more expensive. That's why there's plenty of waney edge consol tables and coffee tables, which you can get out of narrower boards, but relatively few full size waney edge dining tables which require a truly whopping slab. So design your piece as narrow as possible and you'll have a wider selection of boards to choose from. The 700mm you want is a pretty wide board, that's neither cheap nor common.
One way around the width problem is to book match two waney edged boards that are sequential from the same log. Personally I'm not overly sold on this idea but I have done it and it's a common solution to the width problem, here's an example,
http://shop.surreytimbers.co.uk/epages/ ... EWT%201%22
Always avoid a board that's taken from the very centre of the tree. That will contain the pith at the core of the tree. Never include the pith, I guarantee it'll end in tears. Here's what almost always happens to a board containing the pith,
Walnut is a lovely timber, but there are only two or three yards in the country that regularly stock Black Walnut as waney edged boards, so you're much more likely to find waney edged English Walnut. English Walnut is relatively expensive (well over £100 per cubic foot) and suffers from very wide sap bands and can also be prone to shakes and knots. I'd never buy English Walnut sight unseen. Oak or Sweet Chestnut are probably your best bet.
With any waney edged board inspect the sap carefully for worm holes, it's not that woodworm is a serious problem in a centrally heated home, it's more that worm holes always give people the heeby jeebies.
The Oak boards you show in the photo have had most of the sap knocked off, that's very common, but I wouldn't count them as true waney edged boards.
Kilned timber is generally more stable than air dried, but you can make perfectly serviceable timber from air dried. Just proceed more slowly, flatten the two faces and then leave for a few days, then check for any cupping and if there is movement let it dry a bit more.
Good luck!