Thanks for asking this good (and pretty difficult) question, rather than trying to make an assertion; cf. a sibling comment of mine.
tl;dr: that the body is all attached for some time after crossing the horizon is [a] likely and [b] sufficent to justify the notion of stimulation in the feet being processed in the brain, when falling feet-first within a black hole.
Firstly and basically the whole of [b], I'm just gonna assume that nerve impulses are the result of chemicals spat within neurons and between them, all very slowly compared to the speed of light, and all quite local (one chemical change or protein-conformation change at a time, step by step). I don't know the full details, but the relevant thing is that the speeds are slow, and that's the basis for the question ("how does something not faster than light rise within a black hole?").
Now on to what happens to a self-connected body inside a black hole, i.e., a justification for [a].
My nth iteration of an answer to this (abandoned a few because they got too technical or were unsatisfying; really fatigue drove me to a decision to submit as-is or to just walk away from an attempt at a good answer) is that the "rules" of a black hole are that your body's centre of mass cannot climb relative to the centre of mass of the black hole. More particularly, acceleration of the body's centre of mass is a vector (i.e., with magnitude, direction and sense) which is constrained to have the sense be at least slightly inwards at every point inside the horizon.
However, there is no rule about where exactly your centre of mass is found relative to the bits of you stuck to your skeleton and encased in your skin. Equivalently, the sense constraint does not apply to very small parts of your body so long as those small parts do not break the rule that applies to the bulk's centre of mass. (This is another way of stating the universality of free fall version of the weak equilvalence principle, where the vacuum worldline is that of the bulk, the microscopic components of the bulk (atoms in haemoglobin in blood in the aorta etc) are obviously not in vacuum themselves.)
Internal adhesive forces (and other contact/surface forces) win for a while in a battle to keep your extremities from breaking off and taking their own free-falling trajectories, and so (if you are falling feet-first) you could think of your head supporting the weight of your body. As you fall inwards, your feet will feel heavier and heavier and ultimately you become what medical people like to call "disarticulated".
This is a result of three rules:
* A spinning spherical mass becomes oblate. Earth is very slightly narrower between the poles than between two opposite points on the Equator.
* Objects falling onto a spinning spherical mass become prolate, that is longer in a vertical direction and narrower in the directions perpendicular to that.
* Objects dropped above different points on a spinning spherical mass will follow converging trajectories. Handy little diagram: <https://external-content.duckduckgo.com/iu/?u=https%3A%2F%2F...> If we put the stick figure at the equator on the tropic of Cancer instead, the fat arrows pointing towards the centre still converge, just with a smaller angle.
These are all taken to exxtreem in a spinning black hole. The hole itself is slightly oblate. This induces different notions of "straight down" that get weirder as one gets deeper within. The vertical stretch and inward squashed induced on an infaller becomes strong as one gets close to the black hole's centre. And how much inducement there is for parts of a body to find their own notion of "straight down" (the gravitational "pseudo force") becomes stronger than the inducement on them to stay attached to the rest of the body.
If you are falling feet-first, the skin cells on your shoulders want to take their own notion of "straight to the centre", but they are dragged onto your centre of mass's "straight to the centre" because of the forces that stick your skin cells to the layers underneath. Your feet want to fall faster than your hips, but your connective tissue and skeleton keep them from doing that. Your head wants to lag behind, but it too is prevented. Until you split apart (e.g. your femoral artery ruptures, your spine separates, whatever) this structural integrity supports nervous impulses and blood rising from your feet towards your brain. You can still think on your way down.
You could consider this as your internal forces changing the local spacetime geometry to allow nerve impulses and blood to rise upwards; or alternatively you could think of it as your upper bits suspending your lower bits at a higher gravitational potential. The real physics is a complex set of tensors, and with enough initial data you could grind out a full picture with mathematical rigour. You'd then cut down the tensorful field equations into vectors (which way do your various bits get accelerated) by choosing a suitable set of coordinates; probably you'd want to use ones where your centre of mass is always at the origin, or where each of your bits and pieces have their own set of coordinates ("Fermi coordinates") and you do some coarse-graining like averaging. Either way, your body-bits' mutual accelerations overwhelm the tidal forces (and the tidal forces are themselves vectors which we extract from the Weyl tidal tensor in applying the same suitable coordinates).
In support of this line of thinking about how you can still think when you're in a black hole is the "no-drama" conjecture. The radius of curvature just outside the horizon of a supermassive black hole is much greater than that at Earth. Our bodies tend not to be disassembled by Earth's gravitation (in the "tidal" sense; that's that sense which is captured in the three rules above -- a Nasa-produced animation exaggerating the prolation induced by the moon on the Earth's oceans <https://www.youtube.com/watch?v=l37ofe9haMU>), so it would be surprising if they were disassembled by the gentler gravitation just outside a big black hole.
You should just free-fall through a big black hole's horizon without feeling much in the "tidal" sense (your view of distant stars would give things away though, even before you are at the point of no return). For a supermassive black hole you should continue not to notice much for some time (minutes on your wristwatch). Eventually (possibly an hour or so on your wristwatch) you notice and it hurts and your head probably pops off ~minutes later, and your remains "spaghettify".
Unfortunately we don't have enough evidence to select an low-curvature-radius-but-still-near-horizon effective theory, so there are certainly plausible descriptions very different from mine above.
For example, certain physicists reject the no-drama conjecture quite strongly, often because their preferred theories of quantum fields (or strings) predict that the horizon is a tangible surface which supports very high energy radiation. Black hole horizons in general relativity do nothing of the sort; they're just a notion of a point of no return[*], and any particle crossing that point falls inwards, be they super high energy or super low energy or something in between. (The curvature singularity isn't a surface that supports anything either; infallers' remains don't really collide with it or pile on top of it, or rather we can't say one way or another what the case is because the standard equations become divergent. They do not diverge at the horizon though.) In some of those theories you are fried by high intensity gamma radiation before you get to the horizon; in others there is a "firewall" just inside that blows you apart with ~Planck-length radiation. If those are right, there's drama at or very near the horizon, and nothing will be able to spaghettified because it will be disintegrated by radiation.
[*] yes yes, but you (complaining expert) don't know which horizon I mean, and there are many to choose from (Visser, <https://arxiv.org/abs/1407.7295v2>, 2nd paragraph)