“– My penis bends a few degrees to the left in erection.”

Expect either ligament injury or collagen scar at the base tilting it. They usually go hand in hand as when you sprain or injure the ligaments at the base there is also a hematoma present (which later becomes a collagen scar).

“– Cord-like vessel running the length of my penis on the injured side. I originally thought it might be thrombosis, but the urologist said that it wasn’t and I probably just failed to notice it before (I’m pretty certain I would have noticed it so this is bullcrap). “

Sounds like some of your arteries. They are usually cord-like in nature and hard to the touch. The fact that you can touch it through your outer layer of skin makes me believe there is a soft tissue damage involved. (The soft tissue usually fully wraps around the arteries and makes them not directly touchable).

“– The stage between flaccid and erection is when I experience the most discomfort. “

Ever heard of the hourglass penile shape. Better check it out. Definitely indicative of a soft tissue damage and collagen scarrings.

“– Penile erection quality has diminished, especially the corpus spongiosum.”

You said it yourself. Expect softer penile underside, loss of girth, and softer penile glans.

All in all the injury sounds classic and I would recommend the usuals:
Hot-Cold wraps, SR-Cream, other natural oils, meditation, and even infrared lamp exposure.

“The urologist eventually told me that it’s possible it was a partial fracture to the right corpus cavernosum.”

That diagnosis seems wrong to me.. like way-way off the mark.Similar injuries are so rare it’s not even funny.

The ligaments and soft tissues are most likely the ones who bore the dmg.