Let $V_{g,n}$ be the Weil–Petersson volume of the moduli space of hyperbolic surfaces of genus $g$ with $n$ cusps. The fixed-$n$ large-genus expansion of Mirzakhani and Zograf has correction terms polynomial in $n$ of degree $2i$ at order $g^{-i}$, and is no longer asymptotically ordered by powers of $1/g$ when $n$ is of order $\sqrt g$. We prove an asymptotic expansion in powers of $1/g$, uniform in $n\ge0$. For $n\ge1$, its coefficients are analytic in a density parameter on a neighborhood of a compact interval, including the limits $n/g\to0$ and $n/g\to\infty$. Its explicit leading term contains no undetermined constant and has relative error $O(1/g)$; truncation at a sufficiently small multiple of $\sqrt g$ gives relative error $O(\mathrm{e}^{-a\sqrt g})$ for some $a>0$. For fixed $n$ this confirms Zograf's conjecture that the constant in the Mirzakhani–Zograf asymptotics is $1/\sqrtπ$. We also determine, at every cusp density, the asymptotic profiles of the volume ratios $V_{g,n}/V_{g-1,n+2}$ and $V_{g,n+1}/(2gV_{g,n})$ and, in all degrees, the asymptotic ratios of adjacent coefficients of the one-boundary volume polynomial; this answers two questions of Mirzakhani. The proof deforms mixed $κ_1$–$ψ$ intersection numbers into pure $ψ$ intersection numbers along a family whose recursion has nonnegative coefficients, determines the overall constant through Painlevé I without assuming that the Weil–Petersson genus expansion is resurgent, and recovers individual volumes by Gaussian and Poisson coefficient extraction. As an application, the spectral gap of a Weil–Petersson random surface with $n$ cusps tends to zero in probability whenever $n/\sqrt g\to\infty$; this removes the restriction $n/g\to0$ from a theorem of Shen and Wu.