Prior to this when it was on "Auto" the picture was cropped square when the phone was held vertically.
By default, the Splash Page uses the first image in the gallery and the image is scaled to fill (rather than fit within) the Splash Page and, as such, cropping may occur.
You can select a different image to use for your gallery's Splash Page (it does not even need to be a gallery image) via the splashImageUrl configuration option. You could perhaps use an image that is representative of your gallery as a whole and is more tolerant towards cropping when it is displayed in different viewport shapes.
(You could upload an image for your Splash Page to your Showkase 'Library' and then use its URL for the splashImageUrl.)
When the phone was held horizontally, the picture changed sizes as the page was scrolled up and down.
This sounds like it might be due to Showkase dynamically resizing the Splash Page image when the viewport size changes. (As you scroll up and down (in Mobile Safari on iOS at least), the browser toolbars can appear and disappear, resulting in a different viewport height. Showkase will adjust the gallery height when the viewport height changes (just like when a desktop browser window is resized).
I'm not understanding what other setting you may be suggesting for this scenario with the Splash Page for mobile devices?
I was really just suggesting that you might set showSplashPage="AUTO". You could then configure your Splash Page using the available Splash Page options.
The Splash Page itself will still be sized the same as the gallery (when no Splash Page is used) so you'll still have the same problem as before (space above and below in certain viewport shapes) but only with a single Splash Page image. (The gallery itself will be displayed on a page of its own when expanded from the Splash Page.) Maybe with a smaller 'External fit px' value (such as '-100', for example), the spacing on desktop monitors would be acceptable and you could find a suitable image for your Splash Page which would look OK on mobile devices until the gallery is expanded.
Currently I have the "External Fit px" set to -240. Also, would decreasing the logo height be helpful at all?
I'm not sure that this would help. The height of your logo does not change the height of the gallery. A logo with a large height will just push a gallery down the page (and this can be compensated for via the 'External fit px' option).
I think that using an 'External fit px' of around '-100', setting showSplashPage="AUTO" and choosing a suitable image for your Splash Page (one that will not suffer too much when dynamically cropped to fit various different viewport shapes) might be your best course of action.
With an an 'External fit px' of '-100', the space surrounding your gallery in desktop monitors should not be excessive and it should hopefully be a low enough value for a usable Splash Page on mobile devices.