I assume engineers have a way of identifying that point.
We do; it's called a deadline.
All seriousness aside, no we don't. In fact, that's one of my interview questions for engineering managers. It's a trick question in a sense because unqualified candidates think they have a universal answer. We quip that a project in design engineering has two phases: too early to tell, and too late to do anything about it. There is no hard-and-fast point where you markedly shift the approach. Analysis at the beginning of a project is proven to have the greatest effect on cost and complexity, but it happens before enough of the problem has been explored to really know what to analyze. It's the manager's job to break the "analysis paralysis" that occurs from trying to reason conclusively with too little data, and then to get the ball rolling.
The "correct" answer to the LM's problem that the plume deflectors were added to solve would have been to take the LM back to its conceptual mechanical design stage and weigh more heavily the jet duty cycle with its thermal effects. Then the jets could have been positioned to avoid thermal loads on structure over the firing times it became apparent later were wanted for mission planning. But then you would have had just another set of problems that arose from
that systemic arrangement that weren't present in the LM that flew. The urge to analyze extensively follows the natural urge to find an optimal solution. In any significant engineering problem there simply does not exist an optimal solution. The engineer and author Henry Petroski coined the term "satisficing" to address this. Engineering problem spaces are defined by opposing variables that are always in conflict, always in tension. A solution for these variables is ever only "good enough."
The hoaxie that drills down, moving the goal posts or outright changing the character of their claim or throwing up all sorts of chaff in an attempt to find wriggle room.
Which they will eventually find, since no engineering survives all conceivable criticism. But the key is to determine at what level you've found something that merits criticism and how consequential that is to questions like that of authenticity.