I'm not a physicist, so if I've made a mistake I hope someone can point it out.
Eddington-Finkelstein coordinates reparameterise the Swartzchild coordinates (t,r,thea,phi) with (v,r,thea,phi) where v = t + r* and r* = r + 2M log(r/2M -1). Note that r* -> -infinity as r->2M so as r->2M v -> t + infinity. For an outside observer, the ticks of a clock at the event horizon are infinitely far apart. Similarly, dt/dr -> infinity as r->2M.
From another perspective, for an outside observer we're not interested in infalling light rays, we want to know about escaping ones. Pulses emitted from an infalling light clock will appear to us to be farther and farther apart (and more and more redshifted) until they are infinitely far apart at the horizon.
From the perspective of the outside universe, it takes an infinite amount of time for anything to reach the event horizon. A black hole that evaporates on any timescale for an observer at a distance should have an event horizon that retreats from anything infalling.
There does seem to be a conflict between the outside observer and the falling one. It seems to me this is resolved in much the same way the twin paradox is in special relativity. If the infalling observer were to stop just before the event horizon and return to the outside observer, he would find that, while accelerating away from the hole, the outside universe was enormously blue shifted, making up for the blue shift he did not observe while falling inward. When he met up with the outside observer and compared notes he'd find that his clock had been running much slower.
In another way of looking at it, to the infalling observer the universe behind him is accelerating away and he would expect it to be redshifted, but it is not. The universe on the other side (light skimming the event horizon for example) IS enormously blue shifted.