I'll try to jump into this, hopefully being able to help a bit.
As far as I know, Corona doesn't use the subdivide approach of displacement as you'd find it in C4D's AR, Arnold etc.
It's more similar to Octane. I haven't found much on the microgeometry topic and as mentioned I'd rather abstain from giving too much "advice" with my limited knowledge on that topic.
However, I've encountered a very similar problem with Octane and the solution was the angle smoothing(in standalone). I guess this would be pretty much the same as adjusting the phong angle value in C4D.
I've also found this:
https://coronarenderer.freshdesk.com/support/solutions/articles/5000529362It's been a few years since the last time I touched MAX but IIRC, Turbosmooth is basically a subdivision method.
I think one of both solution, phong or SDS could solve the problem.
Now, I know that many people don't want to subdivide their models in fear of losing the shape, even if it's not smoothed.
Luckily, C4D offers Hypernurbs/SDS weighting since v8 and this could be very helpful in such a situation.(assuming it's the subdivision that's needed)
Another thing that is very helpful is to align the vertex normals. There's a small but very useful tool from frostsoft that helps you do that ($1):
http://frostsoft.blogspot.de/2012/01/vertex-normal-tool-plugin_80.htmlWith that, you can align the v. normals to give you the same look of the cube, even if the full phong angle is set.
(assuming the phong angle is the problem)
Also very helpful, a guide to vertex normals: http://wiki.polycount.com/wiki/VertexNormalI hope I could help a bit with the tearing faces problem.