Unfortunately if the presentation is set up at 1920x1080, it will never appear correctly on a display that does not support 1080p. You will need to reconfigure the presentation to a supported resolution.
If you're sure the display is 1080p, this sounds like an overscanning problem to me. Check if the display has any aspect ratio settings or overscanning settings (something like "just" or "actual pixels" or something similar is probably what you're looking for).
I have a client that has a display that does something similar. Their display unfortunately doesn't have any overscanning settings so I've had to resort to issuing a specialised xrandr command every now and then using crontab.