Yes, the projector is 4x3, but the "show" is 5x4, so I think I should be using the latter, but see below, where I cast doubt on using the presets.
I tried your suggestion and the results were a bit strange. The resulting pictures were **smaller** than expected, whereas in the past they'd been bigger. When choosing "Original Size" on an image that, as noted in the original post, had ended up as 1276 wide, the zoom factor was 88.519%. It should have been 99.6875% - 1276 divided by 1280. I think that's because when selecting any of the common (preset) aspect ratios in Project Options, there's no definition (that we can see) of the number of pixels. From the above, it looks like it defaults to something around 1440, yes 1440, not 1400. (Being a multiple of 72, commonly used in printing - it's "pt", the point size, I could quite believe that. Further, 1440 appears in a number of "standard" resolutions. I am only speculating, though) The reciprocal of that 88% number times 1276 comes to 1441 and a bit. That's why I've been using absolute width and height numbers instead of the presets.
My testing involves running the show .exe, pausing on a particular slide, then double-clicking the original image file to open it over the top in Faststone. When running the .exe from MySlideShow Gold, there is absolutely no change in the screen content between the two; they're exactly the same size and both as sharp as each other.
By padding out the originals to 1400 x 1050 and setting the PTE Project output size to these dimensions, I can reproduce the MSS results. I don't need to select "Original Size", because they're all already the correct size for the output - at least the height for my monitor. "Wonderful", I hear you say. However, it's not practical for the (political) reasons already stated. Further, if we were to follow the PAGB (Photographic Alliance of Great Britain) recommendations and buy a 1600 x 1200 projector, we'd have to remake any shows that we wish to use again, otherwise they'd be stretched on-the-fly from 1050 high to 1200; we'd be back to square one. So we'd have to keep all of the originals of all the shows ready to re-pad them to 1600 x 1200 and re-run them through PTE.
As I said in my second post, I need a "don't muck about with the output size" setting, which jt49 says no longer exists. Maybe I should try to get hold of a license for Version 8.