The rotation rates of main-sequence stars slow over time as they gradually lose angular momentum to their magnetized stellar winds. The rate of angular momentum loss depends on the strength and morphology of the magnetic field, the mass-loss rate, and the stellar rotation period, mass, and radius. Previous observations revealed a shift in magnetic morphology between two F-type stars with comparable rotation rates but very different ages. We confirm a similar transition in several well-characterized solar analogs with ages between 2 and 7 Gyr. We present new spectropolarimetry of 18 Sco and 16 Cyg A & B from the Large Binocular Telescope, and we reanalyze previously published Zeeman Doppler images of HD 76151 and 18 Sco to confirm a shift in magnetic morphology near the middle of main-sequence lifetimes. We combine archival X-ray observations with updated distances from Gaia to estimate mass-loss rates, and we adopt precise stellar properties from asteroseismology and other sources. We then calculate the wind braking torque for each star in the evolutionary sequence, and we assess the uncertainties that arise from errors in the observational inputs. We conclude that the shift in magnetic morphology occurs before the age of the Sun, reinforcing the notion that the solar dynamo may be in a transitional evolutionary phase. We suggest that this magnetic transition may represent a disruption of the global dynamo arising from weaker differential rotation, and we outline our plans to probe this behavior in additional stars spanning a wide range of spectral types.