Hmmmmm, I have not made a ton of bendy handle bows. Just a handful, really, but my approach is totally different.
With any bow, I find that I have a higher chance of success if I start with consistent dimensions on my stave. Taking your stave, I would, with actual calipers, work it down to a consistent thickness, full length, if possible. If that is exactly one inch, great, if it is 7/8" great. I would next work the sides until I had the middle 50% of the bow the same width, 1-1/4" in your case, and THEN, I would width-taper the outer 25% on each end down to nock dimensions, or about 1/2". I'd leave a little fudge factor in the width, probably.
Anyway, I know from experience that if I put that on the tillering tree and bent it, it's gonna bend in the middle, and nowhere else, basically. The bend would be parabolic. i don't even need to test it. It can't do anything else. So, I obviously have some work to do on the width taper. I LOVE Paul Comstock's method of controlled, consistent wood removal outlined in the TBB for weight reduction, so I employ it for tapering as well, at least on staves. Boards I can saw or mill.
What I do is mentally or actually (with a crayon or pencil) divide the bow into sections. Mark out 6" in the middle to leave alone, which leaves 28" on each limb. Divide that 28" into 4ths, each 7" long. To taper a bow like this, I rasp the 7" on the end until it is roughed up, then I smooth away the rasp marks with a scraper. I just removed, say 1/100 or 1/64 of an inch. Then I grab the rasp and rough up 14" (two sections) and scrape it smooth. So, now the outer 7" is 1/50 of an inch thinner, and the second section is 1/100. Then, I rough up 21" of the limb and scrape it smooth, then all 28". Then I do the other limb.
I have even gone so far as to use dark crayon instead of a rasp, mark it up, and scrape it off. So, every time the outer section gets 4 passes, the inner next to the handle gets one, etc.. I repeat this a few times until I begin to see an appreciable difference in the thickness at the tips compared to the handle. THEN, I might put it on the tillering tree with a long string and have a look. Remember to never pull it past the final draw weight you want, so you might hang a 50 lb weight from the string, or use Badger's method of having a scale and pulley set-up. It should barely bend at all. If it bends an inch, fine. PROBABLY all the bend is still in the handle, but we BARELY bent it to get a couple inches of deflection at the tips, so it's fine. If it doesn't bend at all anywhere, keep doing the stair-step removal, but include the whole bow.
So, as you work each section, don't freak about a little tool overlap, because that avoids step offs, but on the next series of removals, maybe divide the limb into thirds rather than quarters. Rough and scrape 10", then 20", then 30", into the handle area a bit, and do several passes like that. Then check it on the tree, and go back to quarters.
Eventually, you will start to see that tiny bend in the middle start to spread out along the limbs. When more of the limb starts bending, you can look for hinges and stiff spots, and use the "section" system to tell you what needs more removal. NEVER pull it past that final weight, and it will take very little set. Just keep your eye out for things like uneven limb thickness side to side as you go, and as you get the bow bending further and further, start blending lines, rounding corners, and smoothing step offs or whatever.
I have a longish draw, so on a bow that short I like some bend in the handle, most in the inner and middle limbs and stiff tips to avoid stacking, but tiller is up to you. Since I started doing this, I have had ZERO tillering failures, and neither have the few guys I have taught to make a bow, recently. It's a little slow, but if you never over pull it, and proceed methodically, it works.
