Well... You totally nailed the early 90's "better put a animated gif on the frontpage" homepage aesthetic. I'll give you that. Maybe you should consider doing graphics for the vapor wave scene? They would love you ;]

For actual reference I think this is way more useful:
http://www.anatomy360.info/skull-sketcher/

These are actual scans of skulls that you can lit and rotate in real time.

Who is the artist to these sprites?

First off, what is the light situation? The shading of the tree trunks and fence suggests that it's direct light rather than an overcast sky but it's hard to tell. I kinda get the impression that you didn't have a clear idea to start off with.
Second, what season is it? What is the climate? Unless it is supposed to be some kind of abnormal weather conditions, the grass and leaves shouldn't be quite so lush and green. In fact there probably shouldn't be any leaves at all. If you want to keep them they should atleast be more desaturated and yellowish.
 

I wouldn't recommend Sprite Lamp for pixel art. If you're going to hand pixel things, hand pixel the normal map, that's my idea. Sprite Lamp is not a new idea, it just makes it easier, but also sloppier (as it's auto-generated and not hand pixeled).

Also, about purism: normal mapping can be done (and has been done) on very old machines through palette cycling, there's nothing "faux" about it. We just now have the power to do it in a much more dynamic fashion.

As for the original question, I think I agree that it's probably not going to look good to increase just the framerate for 2.5D. The question is: where does the uncanny value start? From experience, I'm thinking for sprites that big, you CAN go up to 8, but that's pushing it just a little, 6 for a walk would probably be what I go for.

Do you have any examples for sprites with a 6 frame walk?
The 4 frame walks in Doom etc. typically have the passing and down position. Which position would you add for six frames, the up or contact one?

Lol, no rule. But trying to pixel out 12 different directions/angles to include all the animations for each would be a momentous task. I think they could keep to 8 easily an achieve a visibly pleasing effect.

On the issue of 'flatness'. The amount of frames has nothing to do with flatness. Rather what makes a sprite appear 3D is the amount of perceived depth we build into it. Shadows/AA/contrast...etc.

Here is a Unity web build of my project. In which I quickly attached an FPS component to my game so you can walk around and view the sprites. Keep in mind that the Camera is not optimized for pixel use, and the sprites are rendered to appear at a 22.5 degree angle.

MUST USE FIREFOX TO OPEN - Might take a bit to load.
https://dl.dropboxusercontent.com/u/863901/UnityFPS/index.html

Ha, that's pretty cool - and somewhat creepy! It reminds me a lot of a swedish horror novel actually. I guess the little guys can't walk yet?

I must respectfully disagree that the number of frames have nothing to do with flatness - what I'm trying to get at (and no I'm not completely ruling out 8 frame walk cycles just yet!) is that perhaps the limited number of frames feels more congruent with the restricted viewing angles and abrupt movements of the sprites. Say you put a Disney feature film quality animation into a Doom sprite - there comes a point where a too smooth animation coupled with choppy directional changes might cause the effect that looks like you're looking at a video clip moving through space rather than a creature that belongs in Doom. Does that make sense?
I think Hi-res textures look absolutely GARBAGE in Doom for instance. The high level of detail coupled with the rudimentary geometry breaks the illusion and makes it look like everything is built with papercraft.

I guess the point of this thread is that I'm trying to think of ways to improve the 2.5D fps genre by bringing in better quality pixel art and staying on the same technology level so to speak.