What angle should I set the VTA on my VPI turntable?

cleeds,
The sofa analogy ignores the physics of a pivot point. Teeter-totter would be better.

cleeds, slaw, lewm,
I’ll attempt to clarify. Here’s my model:
Put a dot in the center of a paper. That’s the pivot. Draw a vertical line through it. Thats’ gravity. Draw an offset horizontal line through it. That’s the tonearm. Add counterweight and cartridge. Of course we can balance it at 90 degrees. We can also balance it at 45 degrees. Q - How is that possible? What keeps it from just swinging vertical? A - Leverage. Leverage varies with the distance of the cartridge to the gravity line. Maximum leverage at the cartridge is with the tonearm at 90 degrees to the gravity line. The tonearm will usually be less than 90 degrees, it’s in the design. Lower the tail and the tonearm will move further towards horizontal, increasing the leverage at the cartridge, increasing VTF. Because the counterweight is on a much shorter lever the change in distance to the gravity line is negligible.
P.S. cleeds,
I’m playing nice. You should try it sometime.

Some time ago, this issue was discussed here.  The question then was not "whether" VTF goes up when the pivot point is raised, but "how much" does it go up.  Someone did the experiment, and the answer was "not very much", but definitely VTF went UP.  You could repeat the experiment but don't start with VTF =0 as in your model.  Start with a real world situation where VTF is any value >0.  Then you will see VTF go up if pivot is raised.
Also, think of your car sitting on level ground.  It has a given weight distribution between front vs rear wheels.  Think of the front wheel pair as the stylus tip.  Now jack up the rear of the car.  What has happened to the weight distribution?  More of the weight is supported by the front wheels.

lewm,
You must include a pivot in your analogies or they don't apply.  Imagine raising the pivot point until the stylus lifts from the platter.  The arm will balance at less than vertical.  That's because the leverage at the cartridge decreased as the cartridge neared the gravity line and equilibrium was reached (balance).  The VTF is then zero.  It must have decreased.

lewm

... The question then was not "whether" VTF goes up when the pivot point is raised, but "how much" does it go up. Someone did the experiment, and the answer was "not very much", but definitely VTF went UP.

Yes, it goes up, and it's easily measured with a stylus force gauge.

Funny, my experience is the opposite.  I wonder if the answer flip flops depending on which side of parallel the tonearm is.  Above, below or horizontal.  I know what my arm as it's set up does.  Physics isn't my thing and there could be (and most likely are) other explanations I've not considered.  I would love an answer from someone who actually knows.  No one here does, including me.  It's fun and didn't get too sideways.  Cheers!