Considering a photon solar-sail spacecraft with a lightness number in the range [ 1/2-1 ) ( all-metallic sail), this paper analyses a class of heliocentric trajectories, characterized by orbital angular-momentum reversal, delivering a considerable cruise speed (10-20 AU/yr) and allowing a sailcraft to access any celestial latitude [ -π/2, +π/2], depending primarily on the perihelion distance. It is found out that, if the lightness vector is kept constant in the heliocentric orbital frame, the sailcraft in the solar gravitational field is able to decrease, to zero and reverse its orbital angular momentum, then to accelerate while swinging-by the Sun safely and, finally, to get a cruise speed considerably higher than its heliocentric initial one. No planetary launch window is involved. The present 3D theory and its numerical check by a full sailcraft dynamics computer code represent the extension of the two-dimensional theory developed in the last two years. Some examples of deep-space missions are presented. Current and near-term technological aspects are indicated. A demonstration mission to 50 AU and to ecliptic latitude of 20 ° could be accomplished in 5.6 years (perihelion at 0.25 AU). A flight to 200 AU to the heliopause nose direction can last 14.3 years (perihelion at 0.20 AU), exhibiting a launch window of 15 days every year and with a max flight time penalty less than 1 yr.