This is all interesting viz head strikes etc, but the OP's problem looks like a classical case of uncalibrated paper advance, especially the description of needle-width lines running lengthwise across the print.
Yes, so you said, earlier, and you are correct that it is (sometimes) the cause. There are many causes for needle width lines, including head strikes, from the carriage, or debris, etc.
According to HP:
Print the Image Diagnostics Print. See Using your printer.
4. If the printheads are working correctly, go to the front panel and press the View loaded paper key to see the paper advance calibration status. If the status is RECOMMENDED, you should perform paper advance calibration: see Using your printer.
If the problem persists despite all the above actions, contact your customer service representative for further support. (implying that there are other causes as well).
The paper advance calibration does not always solve the problem, particularly if there are other things going on which don't appear obvious. The idea here is to share information based on experience. You have yours (no doubt extensive, and I have mine), having had a Z3100 44" since it first came out, and subsequently two others, (Z3200 24" and Z3200ps 44") in addition to Epsons and Canons in the studio. I have found that the simple fixes are not
always the long term solution with these printers. I have one torn down now, refurbishing it. It's great to come across threads where ALL sorts of issues are discussed, especially when one comes to a dead end. It is great when it is a simple fix, if it lasts.
Discussing printing techniques, and practices, such as issues regarding supporting the material or not is also potentially helpful. Neil Snape worked with HP in regard to this printer, and I believe was one of the first to review it.
I'm not sure why you felt it necessary to reiterate, unless you feel strongly that people should only post along the lines of what your answer would be, and not contribute additional information from experience that may benefit others reading the thread.
FWIW / YMMV