MOST people would want to see what porkpal is discussing, and then comment. That the entire membership of this forum is bereft of the least inkling of interest in images is inconsistent.
At least take a photo of one of "...the long shoots it sends up sporadically..." that you intend to remove, and post it in all its in glory. I'd like to see the WHOLE plant, too - but I'd settle for a well-represented stem.