I wanted to reply to my own message in the event my solution proves to be helpful to anyone in the future.
Windows 7 did not have the appropriate generic USB driver information in its INI/INF files. Only Windows 8 and Windows 10 has the proper built-in drivers to appropriately identify, and allow the proper use of, the Quadro.
Windows update might not work in finding the driver; it did not for me.
In order to fix the issue, one needs to download a cabinet file from the Windows Update Catalog via Microsoft, extract the cabinet contents, and then go to the Device Manager and select Update Driver for the !QUADRO device. Alternatively, uninstall the Quadro in the device manager, reboot or scan for new hardware, and allow Windows to update the driver.
The link to retrieve the cabinet file with the USB driver for Quadro compatibility with Windows 7 is at the following URL:
https://www.catalog.update.microsoft.com…ther%20hardware
You can also simply go to the catalog update site and manually search for "windows phone USB other" or a combination of those terms--the driver itself is intended to allow for Windows 7 to interface to Windows Phones--but it includes the USB information also provided in Windows 8 that allows for seamless device installations. The phone itself has nothing to do with the driver; it is just a description.
The Title of the driver is called "Windows Phone - Other Hardware - WinUsb Device" and is supported in Windows 7, Server 2008 R2, and even Windows Vista.
Download this and extract it to a temporary folder. Manually update the driver by selecting the non-functioning Quadro in the device manager and select Update Driver. Navigate to/choose the location that the cabinet was extracted to, then proceed to install the driver. Windows will discover and read the cabinet contents, and hopefully, query and install the approrpriate driver information.
You may need to reboot or restart the Aquasuite services for the Quadro to begin functioning as expected; this may depend on your system.
I expect that most future hardware devices from AQ will also require this method of installation; fortunately, one need only install the cabinet file information once, and Windows will integrate the information into the local OS driver repository.
(This will not enable any Windows 8 or newer dependent features; this is only a means to find and install the drivers required for the Quadro to properly communicate with an Aquaero on Windows 7.)