The naive combinatorial model-structure conjecture

Let $M$ be the five-point space with two open and three closed points, let $\Lambda$ be the three-point space with one open and two closed points, and let $\left\{M\to\Lambda\right\}^{l}$ and $\left\{M\to\Lambda\right\}^{lr}$ denote the corresponding orthogonality classes. For a finite-space map $p:Y\to B$, write $Y_{{}_p\!\!\searrow}\underset{B}{}$ for its non-Hausdorff mapping-cone object. Naive combinatorial model-structure conjecture. A closed model structure on the category of topological spaces is defined by taking $\left\{M\to\Lambda\right\}^{l}$ as the cofibrations, $\left\{M\to\Lambda\right\}^{lr}$ as the trivial fibrations,

$$\left\{Y\xrightarrow p B:\ |Y|<\infty,\ |B|<\infty,\text{ and }Y_{{}_p\!\!\searrow}\underset{B}{}\in\left\{M\to\Lambda\right\}^{lr}\right\}^{l}$$

as the trivial cofibrations,

$$\left\{Y\xrightarrow p B:\ |Y|<\infty,\ |B|<\infty,\text{ and }Y_{{}_p\!\!\searrow}\underset{B}{}\in\left\{M\to\Lambda\right\}^{lr}\right\}^{lr}$$

as the fibrations, and the compositions of a trivial cofibration with a trivial fibration as the weak equivalences. The conjecture proposes a purely combinatorial model structure on topological spaces, but the supplied text gives no proof or resolution.