If anyone has any ideas about what could give you a sharp spike just around the beamstop, I'd like to hear it.
Kapton tape can produce broad faint rings around 16 - 20 A depending upon where the tape is located in the beam path. Your spike looks too sharp for this, but it's hard to tell on the scale of the plot. Normally, this kind of small-angle scattering does not show up in PX, but it is very clear in SAXS when you have a vacuum flight path etc.
Richard Gillilan MacCHESS Cornell