The relationship between the mechanical, electrical, and morphological properties of annealed films based on short-side-chain perfluorinated sulfonic acid ionomer (SSCI) with an Aquivion structure was systematically investigated using dynamic mechanical analysis (DMA), small-angle X-ray scattering (SAXS), and impedance spectroscopy. Annealing the membranes at temperatures of 140, 150, and 160 °C—above the glass transition temperature of SSCI—and the nature of the liquid phase in the polymer dispersion significantly influence the structural parameters of the membranes, specifically the size of the conductive channels formed by hydrophilic sulfonic acid groups. SAXS and AFM analyses revealed that membranes cast from N,N-dimethylacetamide (DMAA) exhibit a denser, less structured morphology, resulting in lower hydrogen permeability (φ = 4.6 ± 0.7 nmol/m/s/MPa), comparable to the commercial Nafion 211 membrane (φ = 6.5 nmol/m/s/MPa), but with significantly lower proton conductivity (35 ± 5 mS/cm) than Nafion 211 (95 mS/cm). In contrast, membranes obtained from a water-alcohol mixture showed a well-defined structure (SAXS, AFM), with proton conductivity values ranging from 70 to 103 mS/cm, comparable to Nafion 211. However, the hydrogen permeability of these membranes varied significantly depending on the annealing conditions (φ = 5.5–65.3 nmol/m/s/MPa). SAXS data indicated that the membranes had a similar degree of crystallinity (11–13%) but differed in the positions of the ionomer peak and matrix knee, which are associated with variations in the size of the conductive channels and account for the observed differences in ionic conductivity. Membranes annealed at 150 °C, which exhibited hydrogen permeability and ionic conductivity values close to those of the commercial Nafion 211 membrane, were used to fabricate membrane electrode assemblies (MEA). The electrochemical characteristics of these MEAs were investigated at 30 and 60 °C, 100% relative humidity, at both atmospheric pressure and 200 kPa overpressure. At a current density of 1.75 A/cm2, the fabricated membranes demonstrated power outputs of up to 550 and 950 mW/cm2, which are comparable to, and even exceed, those of the commercial Nafion 211 membrane (700 mW/cm2). However, despite the high-power performance, significant membrane degradation was observed after 10,000 cycles in durability tests. These findings contribute to a better understanding of the relationship between the electrochemical properties and the structure of short-side-chain perfluorinated sulfonic acid ionomers with an Aquivion-type structure and are expected to enhance their application in fuel cells.