1/2 syntonic comma meantone
In 1/2-comma meantone temperament, each perfect fifth is tempered by a half of a syntonic comma from its just value of 3/2. This results in minor sevenths being exactly 9/5 (and major seconds being exactly 10/9).
In this system, the "major thirds" are exactly 100/81 or approximately 365 cents, thus bordering on neutral thirds. The fifths of this temperament are even narrower than those of 26edo, which is the most likely candidate for a closed system approximating this meantime.