You don't need to do Li = Lf. In fact, I have no idea why you're doing that. I gave you a list of 3 equations (and an inequality). One of the "equations" was simply D = f(v, h). You actually need to figure out what f is. Basically, you've already figured out the time spent in the air by the flea, t. You also already know it's horizontal speed, v*cos(h). The distance traveled is vt*cos(h), which is:
D = v*cos(h)*t = v²sin(2h)/9.8
So, we have:
D = (Ml/12m)H
D = pi - H
(Ml/12m + 1)H = pi
Ml/12m = (pi - H)/H
m = HMl/12(pi - H)
dm/dH = (1/12)(Ml(pi - H) + HMl)/(pi - H)²
dm/dH = Ml(pi)/12(pi - H)², so m is a strictly positive function of H, and it can clearly be seen that it is strictly increasing. Therefore, m takes on it's minimum value as H approaches 0, and it's max as H approaches pi. Plug in these values into:
m = HMl/12(pi - H), and you get m approaching zero, and m approaching infinity. Well there's a problem

. I think there's some other restriction on H which need to be found. That being, if you have a given D, then there are only certain values for v and h where that will work, and so you will only get certain values for angular momentum of the hair, and so it will only go through certain angular displacements H. Since H is restricted in THAT way by D, but also that D + H = pi, you should be able to limit H to some tigher interval than [0, pi] and so you shouldn't get m approaching infinity. However, figuring out how to restrict H in terms of D "That way" is the ugliest part, and I'll leave that to you.