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

Let me be sure I understand what you are saying, Lutke. You say to place the cartridge on the LP surface at zero VTF, first of all. Correct? Typically when VTF = 0, the cartridge is floating in space above the LP surface, and the tonearm is parallel to the LP surface, else the tonearm is not truly balanced. OK, so in order to get the stylus to come into contact with the LP, I am going to have to crank down the VTA adjuster/pivot point quite a bit from where it would be for normal use, i.e., to play a record. So now I have got that done.  VTF = 0, with the LP in contact with the stylus tip. Now you say to crank down the pivot point still further. Yes, that will increase VTF from zero, because the LP must exert a force on the stylus tip to push it and the tonearm upwards; now the tonearm sits at an angle, with the cartridge up and the counter-weight down. The "VTF" you are measuring is that force needed to perturb the tonearm from its natural position of parallel to the LP surface, when VTF =0. Anyway, any time you want to move a sofa, I am your man. You can be on the bottom as we go up some stairways.

lewm

... you and a friend are carrying a sofa. On level ground, the burden is equally shared. Now you have to carry the sofa up a staircase. Who is working harder? The guy at the top end or the guy at the bottom end? Raising the pivot point shifts the center of gravity toward the stylus. VTF goes up.

Correct. This is basic physics. It’s odd that anyone here would need the explanation, but @wlutke clearly needs some help.
wlutke

I’ve done the work, taken the measurements. Nuh-uh is not a rebuttal. Show me

We’ve explained the geometry and the physics to you. Now it’s up to you to understand.

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.