I'm no Hayek scholar, but this looks like a straw man.

First of all:

Of course his definition of "central economic planning" includes every single corporation employing more than one person...

Straight from Hayek's seminal article:

The answer to this question is closely connected with that other question which arises here, that of who is to do the planning. It is about this question that all the dispute about "economic planning" centers. This is not a dispute about whether planning is to be done or not. It is a dispute as to whether planning is to be done centrally, by one authority for the whole economic system, or is to be divided among many individuals. Planning in the specific sense in which the term is used in contemporary controversy necessarily means central planning—direction of the whole economic system according to one unified plan. Competition, on the other hand, means decentralized planning by many separate persons. The halfway house between the two, about which many people talk but which few like when they see it, is the delegation of planning to organized industries, or, in other words, monopoly.

So by "central economic planning" Hayek means... the government planning all economic activity.

This is what I take Hayek's main points to be (largely from reading The Use of Knowledge in Society, linked above)

• aggregating information is hard, especially for very large organizations
• markets do a good job of aggregating information, relative to alternatives

That's pretty much it, at least that relates to this discussion. Yes, this means there are diseconomies of scale. No this doesn't mean that there aren't economies of scale that are large enough to counter the diseconomies.

note that on my reading, your point about Wal-Mart is a point in Hayek's favor. Wal-Mart, though large, is part of a larger market.

btw, I won't vouch for those who think Hayek justifies extreme libertarianism. He doesn't. But he does rule out central planning ala The Soviet Union.