I am looking for a direct proof that a highest weight representation of $Y(\mathfrak{sl}_2)$ is finite-dimensional if its highest weight is determined by a Drinfeld polynomial.

The results was figured out in Tarasov's paper in 1984 and also was claimed in Drinfeld's paper in 1988.I found a proof of the similar result for the quantum affine algebra $U_q(\widehat{\mathfrak{sl}}_2)$ in the parper by Chari and Pressley in 1991 [Quantum Affine Algebras, Comm. Math. Phys. 142]. My question is: Is it possible to formulate a proof similar to Chari and Pressley for Yangian $Y(\mathfrak{sl}_2)$.

I understand that there is detailed proof in Molev's book. But that proof used the fact that a finite irreducible highest weight representation is a tensor product of evaluation representations. I wish to find a proof based on a direct calculation.

Any comments and suggestions are appreciated.