The experience of a classical infaller (or an observer of a classical infaller) is not really relevant in this story (but please see my final paragraph). Hawking is trying to deal with the AMPS (Polchinksi et al) firewall paradox, wherein an entangled (quantum) pair has one pair partner fly off towards infinity with the other remaining gravitationally bound to the compact dense object that has a horizon.

AMPS strongly suggests that at least one of the following must be false: semiclassical gravity as a valid EFT right to the horizon, gauge/gravity correspondence (in particular AdS/CFT as a useful tool in probing energies higher than the EFT limit), unitarity, and the "no drama" result from General Relativity (which is pretty solidly rooted in the EEP).

Hawking is attempting to preserve all of the above by arguing that the non-escaping pair member ultimately escapes to infinity. In an expanding universe where the non-gravitational field content dilutes away (and consequently cools) leads to a relatively warm horizon temperature for most observers at a distance from the dense compact object. All horizons are observer-dependent (a standard result from General Relativity); all horizons emit a very nearly thermal spectrum (an accepted result from semiclassical gravity, and Hawking did a lot of work in that area, leading to the term Hawking radiation); that spectrum lifts energy away from the dense compact object (an accepted conjecture -- that's black hole evaporation); and when that spectrum is warmer on average than the temperature of the local non-gravitational field content, that evaporation is relevant.

Even in an expanding universe there are local configurations of field content in which dense compact objects persist forever, by exchanging evaporation energy with each other, directly and indirectly; the evaporation energy heats up local diffuse field content, which is then ingested by the black hole, which decreases its horizon temperature (black hole horizon temperature being inversely proportional to mass). An eternal configuration of "dark grey holes" is a possible result, and thus Hawking's proposal is incomplete, since it only resolves the 4-way conflict in particular configurations of an expanding universe. That such configurations are physically reasonable (or even more probable) does not really matter.

Your post correctly captures several aspects of the problem. You expect no drama as you reach an event horizon (specifically the point at which all available timelike geodesics lead inside the horizon), because horizons depend on the details of the configuration of events (including those of the infaller and things that can interact (say, electromagnetically or gravitationally) with the infaller). That is, while the definition of an event horizon is sharp, its coordinate location is observer dependent. As you say, a (classical) infaller crossing the real horizon may not even notice it. However, what about an entangled pair-partner?

Breaking an entanglement transfers mass-energy-momentum (in flat spacetime one would say it releases energy) and in a local theory, that must be sourced by one or both pair partners. If we have lots of such breaking pairs, we have a large amount of energy just inside the horizon -- a firewall.

Hawking tries to step around that by saying that there is no place in the universe where all timelike geodesics point inside a small region of spacetime. That is, all black holes ultimately fully evaporate. And, even if half of a pair is local to a compact dense object for a lonnnnnnng time (many trillions of years), there is no breakage of entanglement, and so no release of entanglement energy. Thus there is no conflict with "no drama", there is no breakdown of semiclassical gravity in the low energy limit (because you don't get probably-unphysical superpositions of the metric sourced by each half of the pairs), gauge/gravity remains useful (because you can still focus on the black hole surface area), and quantum fields evolve unitarily (because nothing stays local to the dense compact object forever).

But if even one black hole anywhere in the universe refuses to evaporate (for instance, because it is so large that it is always colder than the *cosmological* horizon, which also produces very nearly thermal spectrum), Hawking's argument falls apart. The likely accelerating expansion of the universe already imperils his solution for really super super massive black holes, which are not forbidden.

Your analysis is pretty good (for classical infallers); you might want to think about your last long paragraph in terms of an entangled infaller (whose entanglement partner is far away from the black hole), or a classical object made up of entangled particles (again with the entanglement partners far away from the black hole). Additionally, think of the case where the temperature of the CMB alone is always equal to or hotter than the horizon temperature of the (really massive) black hole, both for classical infallers like the one your post thinks about, and for entangled infallers. (You can also consider entangled infallers that "somehow" (there are various mechanisms) appear right at the horizon, with one half going inside the horizon (for some period of time; think about short and really really long periods) and the other half going to infinity right away -- it may help to think of neutrino/antineutrino pairs as they are not likely to interact much with any accretion disk material).