cross cut it to about 2" over the length of the slats you need.
Rip as many 1 1/2" - or so - sticks as you need from it, then rip your 3/8" slats from that (basically resawing it down for each 3/8" slat). The faces of your slats would be the faces of the current board.
Rip it in half to yield 2 4" wide billets. Resaw the extra 1/2" or so off. Then slice off your 3/8" slat material. The face of the slats would be the edge-grain of the current board.
Choose either of the above based on which face has the best lookin' grain. I wouldn't worry too much about the strength of the slats. That stuff is curly, but it ain't super SUPER curly - I doubt you'd have interrupted grain from the curl in 3/8 thickness. You should be okay ... I'd cut a half dozen extra slats, just in case, though