I recently asked how light/photons could get into the present, given that they supposedly don't move through time. I then proceeded to ramble incoherently. This post is to make amends for that. I came up with the following metaphor which may, I hope, make the solution intuitively understandable.
Suppose we imagine an ethereal sphere encapsulating an object, as a visual representation of its 'reference frame'. If the sphere - and all its contents - are moving very quickly (relative to us), then we now say that it appears (to us) that time within the sphere is passing in slow motion. But the sphere itself is unaffected, and still moves just as fast (and, of course, carrying along all its contents with it).
To apply this to the problem at hand: We picture a sphere surrounding the photon, and this sphere travels at the speed of light, and passes through time normally just like everything else (taking its contents - the photon - with it). But time is frozen within the sphere, so that the photon doesn't age.
Problem solved! (Many thanks to Gemma Mason for explaining the basic solution to me.)