Advanced rules for shortening relative clauses with a participle?

The problem with be is that the simple present and present progressive forms have different meanings: the simple present is an ordinary copula, but the present progressive means behave:

The man is funny.
The man is being funny.

The girl, being happy, phoned ... is different: here the clause is equivalent to because she was happy, not who was happy; it modifies the entire main clause, not the girl.

The problem with have is a little more complex. First, it's not strictly wrong, it's just stuffy:

Those having US passports should stand in Line A, all others in Line B.

Perhaps to avoid confusion between the many senses of have, we generally

• restrict participial having in clauses of the sort you're working with to non-possessive/-attributive senses (for example causative The man having his hair cut and experiential people having a good time ); in possessive/attributive senses we use with instead (The girl with black hair, people with U.S. passports)
• restrict participial having as an auxiliary in perfect constructions to temporal clauses (Having finished his dinner, he ...)

The problem is not with the verbs have and be. To see this, consider:

• That's the man being an idiot.
• That's the man being funny.
• The girl having a good time is in the corner.
• The girl having a party is in the corner.

These sentences are perfectly fine despite involving the same lexical verbs.

The problem is also not directly related to the shortening of relative clauses:

• ??The girl who is having black hair is in the corner.
• ??The man who is being happy to be here is in the corner.

These sentences are just as unnatural as the shortened versions.

The problem is the combination of the progressive with a predicate that describes a permanent property (an "individual-level predicate"). Basically, because the progressive describes temporary situations, it's not compatible with predicates that describe permanent situations. Hence:

??The girl who is knowing French is in the corner.

(There's an article here that gives a fuller version of the story, with references, on pp5-6, but it's heavily theoretical.)