I've been trying to square the physics and my experience.

Pedal B flat is the fundamental, low B flat is the 2x, F 3x, mid B flat the 4x, D the 5X, high F is 6X, G half sharp is 7X and high B flat is 8X.

The position your music teacher most likely will have told you to adjust is 2nd position - you play it slightly sharper for an A vs the E or C sharp it's also used for.

Why is that? It's the major 3rd that has the largest variation between just and equal temperament. The A is often a 3rd against the F, is that why?

But it seems to me that it's all the notes on the D embouchure that will be off -- 1st position D on the trombone is 5X the fundamental, so it's justly tuned, not equally tuned, so shouldn't it be the one that needs the most adjustment? I guess all wind instruments have this problem, so maybe I don't notice because usually I'm playing in a wind band with very few equally tempered instruments like piano, guitar and glockenspiel?

Most instruments tend to pitch sharp or flat depending on the partial. I don't recall any music teachers giving advice that specific positions should routinely get adjustments, but instead that notes in a particular partial should be adjusted. For example, F above middle C should be flattened when played in 1st position to compensate for 6th partial tending sharp. Or the G in 2nd position above that F needing to be pulled in a bit to compensate for 7th partial tending flat.

Manufacturers have different philosophies around this as well. I have a vintage mid-1960s King 3b whose partials line up differently and require different adjustment from my modern XO 1634... and both of those horns are extremely similar .508 bore tenor trombones.