It has been almost universally accepted amongst lawyers, who are knowledgeable on the relevant topics, that the “Case-Within-the-Case” Rule (“Rule”) applies to all legal malpractice. 

Actually, this has never been the rule.  It has never been applied to legal malpractice cases arising out of contexts other than litigation. This would include cases involving business affairs, personal affairs, and mixes of the two. It is surely not the case that there must be complete litigation regarding how a contract must be read, for example, before there could be a legal malpractice action. If a lawyer drafts a contract absurdly contrary to his client’s wishes, it doesn’t take litigation before there can be a legitimate legal malpractice suit to determine that there has been legal malpractice upon which a malpractice case can be predicated.

The same point can be made in a more elementary way.  The Rule requires that there be a case previously decided before there can be the pursuit of a malpractice case. In an action on a lawyer’s negligent performance, there is no other case to be within the case being litigated.

One can surely talk about the contract within the case, but that is an entirely different matter.