The authors report on the design of a hybrid transport system for slow positrons based upon the high-intensity magnetically transported positron beam, which existed at the Brookhaven (BNL) high-flux beam reactor (HFBR) in 1986. The resulting modified transport, incorporating an initial electrostatic stage followed by a magnetic stage and completed by brightness enhancement moderation leading to a final electrostatic section, represented the minimum alteration of the existing beam to enable it to be used for crossed-beams differential scattering studies involving a variety of atomic and molecular systems, including atomic hydrogen. A recent proposal for constructing a very high-intensity positron beam at the Paul Scherrer Institute (PSI), based upon magnetic confinement premoderation, has rekindled interest in the conclusions of the study.