I couldn't find any reference to end-grain shooting in 'Modern Practical Joinery' (Ellis, 1907).
However, in 'Turning and Mechanical Manipulation' vol.2 (Holtzappfel, 1847) on page 502 there is shown the usual long-grain shooting board, with an end-stop on the work-rest to prevent the work being pushed off the end by the plane. Holtzappfel then writes, "In squaring the ends, the traverse block of the shooting board is the rectangular gage (sic), and the cross-piece also partly supports the fibres from tearing away; for bevils, corresponding blocks are fitted to it as represented at 'h', but the mitre, or angle of 45 degrees there shown, is the one principally required."
Translated, that says the same as AndyT's example above - the long-grain shooting board is used for end grain, with the shooting board lying along the bench, and the workpiece held transverse to the bench; removable blocks are used to accomodate end angles other than 90 degrees.
(Holtzappel also writes that for panels, the board is first faced and thicknessed, then one edge shot true, then the ends shot and finally the second edge finished to width, thus removing any spalled grain that may have occurred in shooting the ends.)
Speculating now - at some time during the 20th century, the shorter end-grain shooting board we are now familiar with developed to avoid the problems Andy described, but they were either unknown or uncommon during the 19th and early 20th century.
Interesting question! It's always fascinating to see how the craft may have developed over the centuries.