Updating with further discoveries: A distorted crater placed into the landscape seems to work somewhat if it’s combined with a Flow Restructured terrain. The gradient areas, however, get those pockmarked lakes that erosion absolutely hates (the ones that give you these weird lake-topped spires in the terrain) that you get without a Flow Restructure node. Setting the lake-crater-thing to the drainage input or synthesis guide inputs did not seem to have any noticeable effect. Placing a new Flow Restructure node after the results of combining the crater with the previous Flow Restructure node and putting the Create Water node after that makes a river that drops like a waterfall to the bottom of the crater, and then seems to create a canyon that extends to the extent boundaries from there, which admittedly, is a really interesting way to make canyon terrains that I want to explore in the future (in my never ending quest for the perfect canyon scene), but is not immediately applicable.
As a complete aside, if one were to create a bowl shaped lake at the peak of a mountain, would you be able to use that as the sole location for precipitation and effectively make lava flows coming from a caldera? Possibly using the tributary and lake masks as masks for a combiner to add terrain where the rivers are located, rather than having them cut paths, simulating buildup of volcanic rock over time? Just a thought I had while playing around.