TOI-677b is part of an emerging class of "tidally detached" gas giants (a/R*>~11) that exhibit large orbital eccentricities and yet low stellar obliquities. Such sources pose a challenge for models of giant planet formation, which must account for the excitation of high eccentricities without large changes in the orbital inclination. In this work, we present a new Rossiter-McLaughlin measurement of the tidally detached warm Jupiter TOI-677b, obtained using high-precision radial velocity observations with Magellan's Planet Finder Spectrograph (PFS). Combined with previously published observations from the Very Large Telescope's ESPRESSO spectrograph, we derive one of the most precisely constrained sky-projected spin-orbit angle measurements to date for an exoplanet. The combined fit offers a refined set of self-consistent parameters, including a low sky-projected stellar obliquity of {lambda}=3.2_-1.5_^+1.6^deg and a moderately high eccentricity of e=0.460_-0.018_^+0.019^, which further constrain the puzzling architecture of this system. We examine several potential scenarios that may have produced the current TOI-677 orbital configuration, ultimately concluding that TOI-677b most likely had its eccentricity excited through disk-planet interactions. This system adds to a growing population of aligned warm Jupiters on eccentric orbits around hot (Teff>6100K) stars.