enumerative formulas. Two examples include the formulas for the family of reflectable walks in Weyl chambers of Gessel and Zeilberger [@GeZe92], and various approaches using the widely applied kernel method [@Bous05; @BoPe03; @JaPrRe08; @BoMi10]. In these guises, the reflection principle is often a key element in the solution when the resulting generating function is shown to be D-finite[^1]. This is no coincidence: the connection is an expression for the generating function as a diagonal of a rational function. More precisely, in works such as [@GeZe92; @BoMi10], the analysis results in generating functions expressed as rational sub-series extractions, which can be easily converted to diagonal expressions. Unfortunately, the resulting explicit representations of generating functions can be cumbersome to manipulate. For example, much recent work on walks in Weyl chambers has led to expressions which are determinants of large matrices with Bessel function entries [@GrMa93; @Grab95; @Xin10]. Here, we aim to determine asymptotics for a family of lattice path models arising naturally among those restricted to positive orthants – which correspond to walks in certain Weyl chambers – while avoiding such unwieldly representations. This is acheived by working directly with the diagonal expressions obtained through the recently developed machinery on analytic combinatorics 