Solid-state batteries (SSBs) can offer a paradigm shift in battery safety and energy density. Yet, the promise hinges on the ability to integrate high-performance electrodes with state-of-the-art solid electrolytes. For example, lithium (Li) metal, the most energy-dense anode candidate, suffers from severe interfacial chemomechanical issues that lead to cell failure. Li alloys of In/Sn are attractive alternatives, but their exploration has mostly been limited to the low capacity(low Li content)and In rich Li$_x$In (x$\leq$0.5). Here, the fundamental electro-chemo-mechanical behavior of Li-In and Li-Sn alloys of varied Li stoichiometries is unravelled in sulfide electrolyte based SSBs. The intermetallic electrodes developed through a controlled synthesis and fabrication technique display impressive (electro)chemical stability with Li$_6$PS$_5$Cl as the solid electrolyte and maintain nearly perfect interfacial contact during the electrochemical Li insertion/deinsertion under an optimal stack pressure. Their intriguing variation in the Li migration barrier with composition and its influence on the observed Li cycling overpotential is revealed through combined computational and electrochemical studies. Stable interfacial chemomechanics of the alloys allow long-term dendrite free Li cycling (>1000 h) at relatively high current densities (1 mA cm$^{-2}$) and capacities (1 mAh cm$^{-2}$), as demonstrated for Li$_{13}$In$_3$ and Li$_{17}$Sn$_4$, which are more desirable from a capacity and cost consideration compared to the low Li content analogues. The presented understanding can guide the development of high-capacity Li-In/Sn alloy anodes for SSBs.