Just so everyone is aware of what the conclusion of this was, and thank you everyone for your help here.
After lots of discussion with our NI rep and R&D, it was determined that R&D purposefully did NOT implement any VISA capabilities for the NI PXIe-4080 DMM, even the ability to enumerate the device.
They recommended these two things, neither of which are good options for our architecture or requirements:
Use NI's proprietary System Config API to dynamically find the PXIe-4080 DMM. I don't want to transfer my entire framework to this proprietary approach (nor do I believe it would cover all the bases VISA Find does). That's what a standard like VISA is for, which any PXI device should support (at least VISA enumeration/find).
Create an INI/INF file using the VISA Wizard (https://www.ni.com/docs/en-US/bundle/ni-visa/page/ni-visa/usingddwtoprogrampxipcidevice.html), however I don't have access to a Certificate Authority (CA) to make that installable on Win10, nor can I even install the Windows Driver Kit (WDK) on my machine due to IT Security restrictions without particularly difficult approval. NI R&D refused to do the (relatively small) work to create this set of files to fix this oversight.
So at the end of the day, this PXIe device is not VISA capable at all, and they designed it that way. Our project is moving to swap what PXIe-4080 cards we already have to PXI-4070s (which do support VISA enumeration/find/etc.), and future PXI DMM purchases for our setups will likely be Keysight M918xA's, assuming they play nice with NI-VISA on an NI PXI chassis.
I wanted to let folks know that this model isn't fully compliant to the PXI standard (although they tried to claim that they meet the letter of the requirements in a particularly lawyerly way, but certainly not the way any NI customer would read it), and I'm a bit concerned this may be the case with future cards - be aware with NI PXI devices that they might not support VISA anymore.