Hi synclinorium,
Definitely remove the lower segments if you want faster initial growth, you really want to grow them "single file" straight up the post, four each side of the post is the norm... then once at the top let them branch out and fall back to the ground this is the time they know when to flower. If you leave the growing segments your single file grow will slow, however... if you chose to leave them your now got to be thinking these guys are more cutting material let them grow say a foot long make the cut and instant cutting.
** If possible pm me... Id love to get seeds from those "American Beauty" "Purple Haze" or any other variety they are selling in the markets of ripe fruit. BB has massive Pitaya Farm