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We recently described a protocol for computing the potential energy inheterotic M-theory for the dilaton, complex structure and K\"ahler moduli. Thisincluded the leading order non-perturbative contributions to the complexstructure, gaugino condensation and worldsheet instantons assuming a hiddensector that contains an anomalous U(1) structure group embedded in $E_8$. Inthis paper, we elucidate, in detail, the mathematical and computational methodsrequired to utilize this protocol. These methods are then applied to arealistic heterotic M-theory model, the $B-L$ MSSM, whose observable sector isconsistent with all particle physics requirements. Within this context, it isshown that the dilaton and universal moduli can be completely stabilized atvalues compatible with every phenomenological and mathematical constraint -- aswell as with $\Lambda$CDM cosmology. We also show that the heterotic M-theoryvacua are consistent with all well-supported Swampland conjectures based onconsiderations of string theory and quantum gravity, and we discuss theimplications of dark energy theorems for compactified theories.

Stable Vacua with Realistic Phenomenology and Cosmology in Heterotic M-theory Satisfying Swampland Conjectures