Leading-term conjecture for the Jones polynomial of alternating braids

Let $L$ be a positive integer, let $a_1,\ldots,a_{2L}$ satisfy $a_i\geq 2$, and set $D=a_1+\cdots+a_{2L}$. For the braid word $x_1^{a_1}x_2^{a_2}\dots x_1^{a_{2L-1}}x_2^{a_{2L}}$, write $V_3$ for the corresponding Jones polynomial in the variable $s$. Leading-term conjecture. The leading term of

$$V_3(x_1^{a_1}x_2^{a_2}\dots x_1^{a_{2L-1}}x_2^{a_{2L}})$$

is $s^{3D-2L}$. This predicts the maximal degree and leading coefficient for this family of positive-exponent braid words; the surrounding computations support the formula, while the more general combinatorics of maximal-degree terms is noted to be nontrivial.