Honestly an Asiatic style is defined by the use of horn and sinew. I suppose you are wanting to make a selfbow or sinewed bow that has the basic shape of an Asiatic bow, in other words it has siyahs. That would make it a static tip recurve with the static tips exxagerated over what is conventionally employed. The Asians didn't use horn and sinew for fun, they had to use these materials because wood can't take the compression or tension of the kind of hard bend they used in their bows.
You need to do a few things to be successful. The siyahs are no problem, you just either bend your wood or glue on siyahs like the Asians did. Try and use lightweight materials for siyahs, and make them thin and deep so you minimize mass yet have the stiffness you require. No bending in a siyah. Also, you need to have a low enough bend in your working limbs so you don't damage the wood. This means the working limb is going to have to be long enough and wide enough to handle the bend you are aksing of it. The siyahs are going to make it easy to crank those limbs, they are great levers. So you need to know the limbs won't buckle under the pressure. You can use bamboo backing if you want, that puts relatively more stress on the belly of the limb. It does generate more poundage with less wood though.
Some things to avoid. I wouldn't try making very short working limbs. If you use sinew it would let you make a shorter limb with a harder bend, sinew is great for that. Still, without horn you need to make the working limb longer than an Asiatic bow. You also want to use less reflex than an asiatic bow, you'll be stressing your limbs enough by bending, they don't need to add to the pressure by reflexing the working limb. Wood can only take so much. I would also not tiller like an Asiatic, often they bend hardest right off the handle. This will kill your all-wood limbs. I would spread the bend out over your entire working limb, get as close to the fades as possible. Keep in mind, you have fades off the handle AND off the siyahs. This makes for twice the tricky spots as a conventional longbow. But it can certainly be done, people do make static recurves. So many of the static recurves I've seen, have some set in the limbs that pretty much negatees the reflex of the tips. At that point you've lost what advantage you might have gained from a recurve. But since you are wanting a look (Asiatic), you can live with that.
Basically, you want to make a modest design, longer than an Asiatic and maybe a little wider limbs. Keep the rule of having as much working limb as draw length, so you'll want 28" of working limb for 28" draw. No 48" bows here. 56" for a bend-through the handle bow would be my suggestion, and build the handle area up with leather or something bendy to make it look like the stiff handle of an Asiatic composite. Then add the siyahs to that 56" bow. Might make them around 4-6" instead of the longer siyahs you see on a lot of Asiatics. Try and keep the poundage reasonable. It'll still look like what you want, but it'll be stable. It might always have a bit of kick from the mass of the siyahs. But we're going for looks here.
Good luck, and keep us posted.
