As an alternative to all the above, perhaps consider a blade made with natural composite fibers. They are hard to find commercially, but they do deliver the playing feel you are looking for. They have slightly greater lateral / torsional stiffness than a typical 5-ply to 7-ply all-wood blade, but still typically retain the softer playing feel (though this is just a guideline not a rule... Really it depends on the outer ply you use as well).
The first mass-produced natural composite blade that comes to mind is the Andro Flaxonite ( it came in two models- Driver or Cruiser). It was a great blade that used flax fabric rather than carbon / alc / kevlar / fiberglass etc, and like all natural fabric composites it offered a feel somewhere in-between all-wood and synthetic fiber composite blades. Andro sadly discontinued their Flaxonite range a couple of years back, but there are still some unsold new blades floating about in the shelf stock at various TT retailers (blades have a long shelf life -they can literally hang about in a retailer's unsold stock for years).
Failing that (and forgive me for any glaringly obvious self interest here) I have made natural composite blades myself several times before, examples of which can be found on the photo gallery page of my website. (PM me for a link)
In all fairness, natural composite fiber blades really aren't that difficult to make - any competent bladesmith / custom blade maker who can make a regular synthetic composite fiber blade, should also be able to produce a natural fiber version for you.
As for what type of fiber to use, any of the common bast fibers should do the job okay (ie: cotton, flax, linen, jute, sisal, etc.) IIRC I also heard talk somewhere of some other natural composite fabric blades being produced by one (or some) of the smaller Japanese TT blade houses (I think one of them was Darker?) ...which I understand were using natural fiber composite layers reinforced with a nanocellulose-doped biodegradable resin. These should also (in theory at least) provide that 'in-between' playing feel you are looking for.