Ok, this is something extreme, just to see if we can use a tank to kill a fly.
First of all we're going to fully uninstall your monitor:
.- Right-click on the System icon on your desktop and select "Management" (or "Manage", I'm roughly translating from italian)
.- In the new window select the "Devices management" (or whatever it's called in english) branch
.- In the right pane find "Monitor" and open the branch
.- Right-click on the monitor model and select "Uninstall"; if there are two with the same name, uninstall both; if it gives you the option to uninstall drivers too, tick the box
Ok, once we're over with the noob stuff, let's move to the pro:
.- Start -> "Run..." -> gpedit.msc -> Enter
.- In the new window, in the left pane open these branches: "Computer Configuration" -> "Administrative Templates" -> "System" -> "Device Installation" and select "Device Installation Restrictions"
.- In the right pane find "Prevent installation of devices not described by other policy settings" (or something alike) and double click it
.- In the upper half of the properties window are thre options, select "Enabled" and click "Ok"
Now you can restart your PC and Windows wont be allowed to install any device, either automatically or manually. This will prevent any unwanted driver to come in and mess up.
Now once again:
.- gpedit.msc
.- "Device Installation Restrictions"
.- Double click "Prevent installation of devices etc etc...."
.- Set it as "Not configured" (or whatever it is in english)
No need to restart the system again, the policy is read every time you install something and not pre-loaded at startup. Now you can manually install your monitor with the driver you prefer.
If it still doesnt work, we can try forcing the generic driver this way:
.- Right-click on the System icon on your desktop and select "Management"
.- "Devices management" from the left pane
.- Find the monitor in the right pane, right-click and select "Update software driver..." or....well, you know!
.- You should see a new small window with too big buttons: one is for automatic driver search and one is for manual installation; chose the manual way
.- Now you're given two options again, specifying a path or manually chosing the driver you want to install; go for the manual selection
.- Now you're given a list of compatible drivers, which should be very short because of the ticked option box that says something like "Show compatible hardware only"; untick it
.- Now you have a full list of manufacturers in the left list box and another long list of products in the right one; right?
.- In the left pane go to the top of the list and find "(Standard monitors)"; select it
.- In the right pane you now have a whole list of very generic monitor models; select the one that says "Generic Plug and Play monitor"; watch out, there's also a "Generic non Plug and Play monitor", select the right one
.- Now that you have selected the right monitor (Generic Plug and Play) click "Next" and it will install the driver
Obviously you can use this method the other way around, to force installation of the HP driver over the generic one.