There is no "wrong workflow". You can suggest better workflows, show errors that are due to specific workflow, etc..., but you can't call one workflow "wrong".
OK, I'll take that. But when you get down to it, working general to specific with considerations for all parts at all times leads to more cohesive, unified results. This is not always the best plan, say for a large painting, sometimes it's better to work up the focal points with only a vague consideration for subordinate elements (not how i work but ok). Certainly in the finishing these important parts get more attention in most cases.
In an animation though, this is not generally the case.
You could take the best flower, the best milk, the best spices, and the best chicken, but if you don't follow a recipe you're only going to get a pile of food and not a meal.
Nobody will ever look at something and say "well it seems disjointed as a whole, but how good is that left leg movement!"
Not even that, but you can't even have good left leg movement unless it's relating to good body movement! Even if you are successful at first, when you work on the rest, any and every change will affect the movement you had until it no longer looks good with what you've got.
Animating by pieces only works in select cases, particularly (as you mentioned) easy things, and things you've done a thousand times, or when you grind grind grind away blindly and like all blind methods get lucky sometimes, and this can be more creative as Gil mentioned, but is unsuccessful 99% of the time. I recommend this aimless, searching method as a way to expand your mind beyond traditionally safe ideas - ideas you should
still know because they work and they are fundamental.
Is success always important? No, of course not. I fail all the time and am better for it. Challenge alone can spur growth. But failure should generally lead to successful practices. That is (generally) the goal of critique and it's the goal I hope to help you towards.
The reason I posted the Professor in the first place was to discuss how hard it is to animate someone moving at a slow pace.
The point of critique, which this board is partly responsible for showing me, is that you shouldn't have a preconceived agenda for your critics, but be
open to their suggestions. I benefit the most when I don't direct the conversation.
I feel bad for posting him at the state he was in, I know I won't do that again.
Sorry to have discouraged you. But really, I think you should have posted it earlier, so that we could have helped with the overall movement. Continuing with your current methods is not producing results.

Why does his neck move like that? Can he magically stretch it without shifting his shoulders? Why is one arm so much faster than the other, particularly if it is carrying some weight?

He's just dropping a lightweight motion by a pixel, which isn't going to make it a heavier animation. In both of these cases you're moving solid, highly-polished blocks of work around and hoping they fit together better if you push and squeeze. It doesn't work that way.
What I'm asking, if you REALLY want these animations to wok out, and what's better than tweaking and adding to two animations that already have broken systems of motion and trying to make them a system, is to start from the beginning with a more comprehensive method that is proven to work. Is that a tall order? Yes, it's hard to dump a lot of good work, and this is very good work. But it's work that isn't working out, and the fact that all that effort and polish and great stuff isn't working out is, I think, a great argument for nailing down the greater movement first before investing each piece with such attention, so that when you get around to those efforts, you know they are going to work properly together.