PS. I like Zoom to Fill Frame but it renders any portrait orientation photo unusable as it zooms it to the very center of the photo.
You have the option to fill the grid-
But this will automatically crop any images that are not of the same aspect ratio!
You can re-position the image withing the grid by holding the Space-Bar and mouse dragging.
You will need all the Guides set to zero-
Another problem reported in other posts is that 'small' images (eg 200x300pixels) will not expand to fill the frame. (This may be a Lightroom bug!) The only work-around might be to Export a small image to one of a larger pixel size, and use this image in the slide-show.
If I have understood your requirement correctly I'd suggest using LR/Mogrify2 as an export plug-in to create jpeg files http://www.photographers-toolbox.com/products/lrmogrify2.php Using Mogrify has a facility to pad excess canvas borders in black (or your preferred colour) so that the unused areas are not distracting. Essentially set the measurement control to a maximum matching the vertical and horizontal dimensions of the display aspect ratio at the preferred resolution, with the overall canvas constant at the maximum possible dimensions. It's difficult to summarise but you can output landscape and portrait formats so that one dimension always covers the maximum possible and simulataneously centre the image in the other direction - this stops images jumping around because excess borders are dark and even and each image uses maximum space. (There might be an issue of some images are too small/lowresolution to match the maximum chosen dimensions in pixels - so try some small ones first.)
Then use another program to display the slide show or if you prefer re-import to LR. Once you have the hang of using Mogrify it is relatively easy to break a large quantity into a series of batches, as a workflow this may seem long-winded but it gives you complete control. The only concern becomes sorting sequence(s) (or numbering them correctly) first time to create the desired show. (Note: installation on a PC requires ImageMagick.)
Good luck if you chose this workflow