It strikes me that, while this is not precisely what you're asking, Law French I think it might be argued fits the bill.

While French, of course, was the everyday language of the upper class in England from the mid-11th to the late 14th century, and was therefore naturally the language of the Law, it can hardly be called a "constructed language". But after this time, it might be said that, divorced of all real connexion with French or Anglo-French culture, Law French came to be something like an invented language based on natural French. It was certainly a group project (lawyers and judges, all others need not apply).

Later examples are both humorous and instructive:

Richardson Chief Justice de Common Banc al assises de Salisbury in Summer 1631 fuit assault per prisoner la condemne pur felony, que puis son condemnation ject un brickbat a le dit justice, que narrowly mist, et pur ceo immediately fuit indictment drawn per Noy envers le prisoner et son dexter manus ampute et fix al gibbet, sur que luy mesme immediatement hange in presence de Court. -- Sir George Treby

ahem

Perhaps Law French might best be called a deconstructed language?

About all that's left in modern times are a few set phrases, mostly in Parliament:

La reyne (or le roy) remercie ses bons sujets, accepte leur benevolence, et ainsi le veult -- (The Queen/King thanks her/his good subjects, accepts their bounty, and wills it so)

La reyne (or le roy) le veult -- (The Queen/King wills it)

La reyne (or le roy) s'avisera -- (The Queen/King will advise)

Soit fait comme il est désiré -- (Let it be done as it is desired)

Even in the USA, we still hear oyez, oyez, oyez when court comes to order.

Some interesting notes on Law French, especially pertinent to the question:

"The effort of reporting English speech in French was not merely an expression of affection for the past, for in the long run it probably saved a lawyer more time and trouble than was taken to learn it. ... The formalised French phrases used in the year books gave him a shorthand ready made and adapted for legal purposes."

"To the linguist, Law French is a corrupt dialect by definition. Anglo-French was in steady decline after 1300. ... (That English lawyers could seriously complain that French, spoken in France, had deteriorated considerably as compared to its use in England) is in itself a clear demonstration that by the middle of the fifteenth century there was a marked difference between the French of English lawyers and the French of France."

A Frenchman living in England during Elizabeth I's reign noted of Law French "...now it seemeth that almost there is no language more far from the true French, then the French of our lawes: There being almost no word, which either by intermingling, or adding, or diminishing, or changing of a letter into another, they have not altered and corrupted."

"The lawyers also took what seemed to be a perverse delight in pronouncing Law French as if it were English: indeed, 'their pronunciation differeth so much from ours (French) as it is impossible for a Frenchman to understand them'.

"Few of those who used French paid the slightest attention to grammar or vocabulary."

All taken from J.H. Baker's Manual of Law French