Here are some updated pictures: https://imgur.com/a/jgllDk8

One plant appears to be well on its way to death. The other looks okay. They're planted about eight feet apart in similar conditions. Any ideas are greatly appreciated.

Please post photos directly here (as well as on imgur if you want). Many folks aren’t going to go to another linked site.

How does the soil feel a few inches down? Have you checked the potting soil moisture in the original rootball?

For now, give it some shade to reduce transplant shock and actually check the soil moisture both in the rootball and in the surrounding soil. Rain is usually not enough for new plants, but without checking, you cannot be sure.