Bullvalene is the archetypical "shape shifting" molecule, undergoing continuous Cope rearrangements in solution at room temperature at a rate of about 3 kHz. In the confined spaces of an scanning tunneling microscopy break junction (STMBJ) setup, isolated bisarylbullvalene molecules have recently been shown to exhibit very restricted isomerization and slower interconversion rates. The restricted number of populated bullvalene isomers displayed large variances in conductivity with the confinement to manifest high piezoresistivity. Herein, the confinement is increased by forming self-assembled monolayers (SAMs), focusing on measuring the resulting electron-transfer rates, as well as identifying viable SAM structural possibilities. First, bis-4-phenyl acetylene bullvalene was synthesized and its SAMs were produced on Au(111). Redox active ferrocene tail groups were then attached via a copper catalyzed azide-alkyne cycloaddition (CuAAC) to enable electrochemical measurements of SAM coverages and electron-transfer rates. The results are consistent with only a single isomeric form being present on the surface at any one time, with its nature varying with monolayer coverage density. Density functional theory (DFT) simulations indicate that a combination of steric interactions induced by the bisarylbullvalene substitution, combined with head group and SAM packing effects, results in this coverage-dependent isomeric selectivity. A small number of very different types of SAM structural possibilities are identified. These findings provide a pathway forward for the exploitation of bullvalene's constitutional isomerism in facilitating nano-electromechanical systems (NEMS).