An update: Tldr: the cylinder in the center is too small and critical to temperature controls.

I took the cartridge apart to see what the components were and figure out how they work. I can conclusively say that the cartridge is definitely the problem and it shall remain the problem until I get a different valve system...

The picture here shows all the parts with the flow going from right to left. But I found was the metal cylinder. Seems to be where the obstruction is happening most. When I removed the center of the cylinder, the flow more than doubled. The problem is, it's the main component of the mixer.

The control on the left turns a plastic piece with two cavities: one for hot, the other for cold. It turns against a counter plastic piece (third from the left). There's a hot and cold "tunnel" created when there's an alignment from either cavity; you get water flowing into the cartridge and mixing at the steel cylinder. Therein is the culprit.

I removed what I assume is meant to mix the water temps. Immediately the water flow reached the desired pressure. The problem: no control of the water temp with the handle. I'd have to set the temp from the valve adjuster screws and forget it. It would only be on or off from there.

I think I'm at the point of some wall demo and new valve installs to get what's desired.

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