Since Windows Phone devices use MTP when connected to a PC via USB, they don't show up as true mass storage devices. One of the limitations of MTP appears to be that files added to the device (such as new photos taken) after USB connection was made are not accessible from the PC until the phone is reconnected. As such, it would seem that what you want to achieve is impossible, at least within the parameters you specified.
Seeing as only the phone itself can see the new photos, the only way to do what you want would be to connect the phone to the internet and configure it to auto-upload photos to OneDrive. The PC can the download them automatically. If the location where you're doing the slideshow doesn't have WiFi, you may be able to add a wireless card to the PC and create an ad-hoc WiFi network, then use that to share the PC's internet connection with the phone.
Alternatively, if you're not dead-set on Windows Phone, you might consider Android. Although newer Android devices also connect over MTP by default, there might be ways to enable standard mass storage mode. Of course, if image quality is paramount, few Android devices will be able to compete with the Lumia Icon, and those that can (e.g. high-end Samsung Galaxy devices) might exceed whatever budget you have for this endeavour.
This sounds like something you'll want to do from the PC side. Since the phone is going to show up as a portable device, you can simply use any of a number of file syncing utilities to automatically copy any new photos from the phone to a folder on the PC. Alternatively, you might be able to start your slideshow directly from the phone's Camera Roll folder, assuming of course that the phone is never disconnected.
To automatically upload the photos to OneDrive, simply use the official OneDrive client and point both the file sync utility as well as your slideshow to a subfolder of your choice in C:\Users\username\OneDrive.