And then I find out the "classic" microfacet BRDF doesn't even conserve energy in the first place.

This is your problem & it's being taught to you by your teachers(book/paper authors etc) who are going by outdated philosophies. The most important thing is photographic validation and it's the reason why techniques like energy-preserving Oren–Nayar (EON) are honestly extremely boring & overrated.

Two games really prove how important photographic validation is: MGSV & Callisto Protocol

Both games store photographically inspired BRDF parameters (not in g-buffer, but in separate LUTs) for materials, one looks better than most games put out today & one remains peak rendering quality.

So many people spit on burley diffuse because it isn't "energy conserving" yet it looks a thousand times better than Lambert because it emulates quantified material differences (retroreflection, diffuse fresnel) but many leading engineers will downplay implementing burley over lambert because of "it's not worth it because it's not energy conserving".

It's highly suggested that you watch this presentation. A major goal for development was using the the simplest arithmetics as possible yet nothing on the market has come close in a quality/performance ratio: https://gdcvault.com/play/1029339/The-Character-Rendering-Art-of

The most physically accurate results (callisto BRDF) were not achieved by "following the books", it got done by referencing the the advice of competent artist which many of the authors of the content you read from are not trained in. They are just programmers at the core.

So again, what's more physically accurate:

A: The method that follows a theory created the the limited scope of our analyzation methods.

B: The method that actually looks like reality (confirmed via photographic error)

Sometimes it can be both like callisto/burley as both are maybe not "energy conserving" but still go through great lengths in matching well documented/quantified properties of real materials.

Do not let people who bombard you with "I have 10 years of experience in this or that" distract from logical conclusions or dictate what is or what isn't "correct" as many of them never use their eyes like artist do. To make things clear, the artist ability to reference reality is the complemented skill, NOT the creative aspect as throwing in random "imaginary" behaviors is not the intended goal for what we are discussing here.

it tells me Schlick-GGX isn't physically based. I cried. 

Hopefully after studying the information & philosophies here will help you look at things with a more progress oriented perspective.