I just started re-reading the Blue Book of Grammar and Punctuation, and came up with this poem to remember “Rule 2.” from the “Adjectives and Adverbs” section:

Roses with noses smell sweetly,
While those with no beak just smell sweet.

Sincerely,

Brian Jones

Rule 4 says, “Generally, hyphenate between two or more adjectives when they come before a noun and act as a single idea.”

In the phrase friendly-looking man, “friendly-looking” is a compound-adjective describing the noun man. It is not an adverb. That is why there is a hyphen.

Rule 5 states, “When adverbs not ending in -ly are used as compound words in front of a noun, hyphenate. When the combination of words is used after the noun, do not hyphenate.”

Since all of the examples you gave do end in -ly, this rule does not apply to them. Only compound adjectives—adjectives that act as one idea with other adjectives—get hyphenated in front of nouns. According to the Chicago Manual of Style (7.82), “Compounds formed by an adverb ending in ly plus an adjective or participle (such as largely irrelevant or smartly dressed) are not hyphenated either before or after a noun, since ambiguity is virtually impossible.” Thus, in your examples, the correct usage would be:

highly impossible solution
highly developed technology
highly sensitive teeth
closely held corporation

family-owned estate (family-owned is a compound adjective).