Red oak and hickory will be fine. I make a lot of fabric-backed red oak recurves by cutting out a pyramid limb, then recurving the tips about 1/5 the limb length. I boil or steam and clamp to a form. Then narrow the tip side to side, but do your tillering from the belly, mostly below the bend. If you thin the bent portion, the recurve will pull out.
I use a wide limb for oak, about 2-1/2" near the handle, and make my recurves gentle enough to be "non-contact" recurves, meaning that when strung, the string is still only touching at the nock, rather than laying in the recurve portion of the limb.
Pat is right, though. Even with a 2-1/2" wide limb and 66" or so long, the oak usually takes some set, creating a deflex recurve, and I haven't really gained much. Making a slightly Perry reflexed, narrower, longer pyramid bow might be just as good in the end.