What are these bladder snail parasites?
I have finally figured out what these are, and it turns out I greatly misunderstood their relationship with snails.
These worms are annelids of the genus Chaetogaster, specifically Chaetogaster limnaei limnaei.

Source: Page 653 of &quot;Fresh-water biology&quot; (1918)
Ch. l. limnaei is unique in its genus in that lives on the bodies and in the shells of snails, including Physa spp. like the Physa acuta snails in question. While the relationship was originally thought to be parasitic by early researchers, it turns out that it's actually commensalistic (or even mutualistic in some scenarios).
From this vantage point the worms feed on various microorganisms, such as rotifers and algae, and small particles stirred up by the host snail scavenging for food. They also feed upon the cercariae and metacercariae of fluke species that parasitize the snails, even able to protect the snails from getting infected in the first place.
That said, it's not all good-- Snails with heavy infestations of Ch. l. limnaei have been shown to be less active, spending more time in their shells rather than out and foraging for food (Stoll et al., 2013). Additionally, worms have been experimentally shown to consume tissues of their hosts when food is low or nonexistent (Stoll et al., 2013).
To respond to a few points from the question:

These worms are highly specialized, and do not seem to affect ramshorn or pond snails, which I have numerous of in the same tank, in the slightest. It's only the bladder snails that end up infested.

Ch. l. limnaei is not restricted to bladder snails, and will happily live on pond snail and ramshorn species. It's possible that the bladder snails had more severe fluke infestations which the worms found preferable.

My theory at this point is that the young penetrate snails, grow inside of them, emerge and hang onto the host for a while, and then eventually dismount as free-living adults. Adult worms seem to be independent, while smaller worms hang off of the host the snail (feeding off of it?) until they're large enough to live freely.

This worm is able to reproduce both asexually through budding, but also sexually as shown here. Sexual reproduction often occurs in the winter, where the worm lives freely and reproduces sexually before returning to snail hosts in the spring.

I would like to eliminate these worms if possible

I found a blog post by someone struggling with the same problem:

One day (do not know it exactly, probably few months later) I noticed that all worms disappeared. I did not know why they were gone.
Later I found the reason in the 1974 thesis. Chaetogaster limnaei limnaei is highly sensitive to temperatures above 24 °C. Such a temperature reduces or completely eliminates these worms. Therefore, If you transport worms from their natural environment to your tropical aquarium, there is no need to worry. If you have aquaria with aquarium heater, they are bound to be killed by high temperature. Worms are killed in summer heat as well.

This seems to be accurate, as with the onset of the summer heat, I no longer have any of these worms present on my snails. Now knowing what they were, it almost feels like a shame-- They were protectors, not foes.
References

Density-dependent relationship between Chaetogaster limnaei limnaei (Oligochaeta) and the freshwater snail Physa acuta (Pulmonata)