Universality of the oriented minimum spanning tree limit for positive continuous weights

Let $(W_{\vec e})_{\vec e\in\vec E}$ be i.i.d. weights with continuous distributions supported in $(0,\infty)$, rather than i.i.d. Exponential$(1)$ weights. Let the main theorem assert the stated local-limit relationship between the oriented minimum spanning tree and the uniform spanning tree on the complete graph. Universality conjecture. The main theorem is true for i.i.d. weights $(W_{\vec e})_{\vec e\in\vec E}$ with continuous distributions supported in $(0,\infty)$. This conjecture proposes that the result is universal over continuous positive-support weight distributions; the supplied text gives no resolution.