I print from PDF's quite often, and have had similar problems with my color HP printer, where objects might print somewhat randomly on the page. I have never experienced this same issue with the HP monochrome printer so, in my case, the problem is the printer.
I resolved the problem by exporting the file as a JPEG and opening it in Illustrator, then save it as a PDF, which, because it has now become a bit-mapped image, prints correctly.
Sure hope you find this helpful. I have attached the bit-mapped PDF.
Slim Pocket Wallet exported as JPEG.pdf