With the Z3100 selected as your printer, click the reset button to the right of the "Properties" button on the Printers and Settings tab and choose "Printer" to reset the settings for your Z3100.  Then click the "Properties" button and set your desired settings in the driver (do not load any saved setups or jobs as those might be incompatible now).

If you still have a problem, it may be related to some serious printing bugs in the last two updates of Windows 10.  My inside info says MS should have that fixed by the end of January.

As for Photoshop, keep in mind that PS doesn't "print" anything: it dumps the edited/open image to the driver and says "here... you do it".  Qimage actually optimizes the data and manages data flow to the driver which is a completely different process so the fact that you can get a print from Photoshop doesn't mean your driver is working properly; it could be subject to the latest Windows 10 bugs (or HP driver bugs).

Regards,
Mike

Yikes!  Sorry to see you are falling into some of the latest Win10 bugs.    MS really seems to make printer compatibility worse with each update.  I've reported what I can and provided detailed bug logs to my contact at MS and all I can say is that they appear to be aware of the problem and are working on pushing fixes in January.  I ran into some really obscure problems here, with drivers failing at the OS level and weird problems like the driver stops responding on certain models when you set the paper size to larger than legal size.  Weird stuff.  But fortunately (for me I guess) they are not Qimage specific.  In the instances I've found, if you run into the settings that cause a problem, not even MS Word can print and you can't even bring up the printer properties (driver).

Mike

John,
This is Fred  here until Mike gets to his office. I am an early riser.

I found this.
  https://h30434.www3.hp.com/t5/DesignJet-Large-Format-Printers-and-Digital-Press/Designjet-Z3100-appears-to-work-in-Windows-10-64bit-using/td-p/5711472

I realize that it sounds like you are facing a corrupted file that will not allow overwrite, or a registry entry that is not permitting an over write, so it is likely this W 7 driver will not help.  Worth a shot though. (The fact that it is a W7 driver might write to the registry in a different spot)

I wondered what I would do.... In my case the answer would be to restore a system backup.
Never mind Windows update uninstall, have you tried a SYSTEM RESTORE ?
Unfortunately many users turn this off due to disk space use.
If yours is on... see screen snaps,  by all means reset to an earlier date. You will not lose any files, but devices and registry and drivers will revert.
Now the 64 dollar question. Do you do backups of your computer on some sort of regular basis? 
I backup my entire C:\ drive on to a separate drive every 4 days.
This really resets all like a time machine.

I suspect the registry has a corrupt entry for the printer.
I feel confident that Mike might know what registry key to delete.

I finally figured out how to send a text message, so I will try to alert him as early as I can.
Fred

Mike:
Just wanted to let you know that HP told me the Z3100 is no longer supported, and no plans to update any print drivers. Will try and get my computer back to an earlier version of Windows 10, or use an old Windows box to drive the printer.  Appreciate the help.

John Nollendorfs

Fred:
Problem is, I can't get by the "unsigned driver" problem. I've tried just about every method on the web, and can't seem to get it to work.

John Nollendorfs

I have it in Windows test mode, but the dialog box still pops up when I try and start the HP installer. Might  have to re=install windows?

John