I would say this would be illegal.
Although a private vehicle is private property, it is considered "public" for common decency purposes. For example, for the communications statute, a john's car does not count as a private place. This is because in a vehicle, you are easily viewed by the general public (bystanders).
In this case, although the solicitation and transaction may occur in private, the actual act occurs in a public place. This may be considered sex in public, lewdness, etc.
You could argue later, in court, that because the limo has tinted glass it is not visible to the public. But the cops won't care. Is it really worth the time, cost, and humiliation?