phoenixart

Check the Curves Tree panel.

Right-click on the scale icon 

So, as I suspected, it's indeed a problem with AMD/Threadripper CPUs:
My threadripper worked ok, but I can't say it met the expectations. At the time when it came out, on every 3d forum, it was welcomed as the Intel killer. Another example of how fuss not necessarily equals facts.
X-Particles for C4D suffered the same fate, painfully slow compared to cheaper Intel CPUs.
I've been an Intel user for years, the 1950x was my first AMD CPU. I'll surely stick to Intel for my next build.
To be clear: I'm not saying AMD is worse than Intel. I'm saying it performs worse with the 3D software I use on Windows. That's an important distinction because, at the end of the day, it doesn't matter if something seems more promising on paper. What matters is how well that piece of hardware is optimized for the OS. 
 

Close the Material Control Panel
 
Then pick a color, and with the fill tool selected, click on the mesh.

@Carlosan
I added a temporary solution to the conversation above:
phoenixart — Today at 12:55 AM
A couple of workarounds for what I'm trying to do.

The simplest, is to change the blending mode of what I wanted to use as a clip mask, to multiply.

The other method is to use Align Colors.
So, now I can start from an AO pass, paint on it if I need to, and use it sort of as a curvature map without going the Smart Materials route.
 

Thanks for the link, @Carlosan
That helped.
I've created a few brushes which I'm going to share, just in case they may be useful to other users, and to see if they're working OK on other systems.

Under the edit menu: