Entwined fiber-filled filament stops extruding after a few layers
I've managed to get a successful print! The key was to keep the material moving quickly. The settings I've customized are as follows:


Print Speed: 70 mm/s
Layer Height: 0.4 mm
Default Printing Temperature: 215C


...and perhaps not as necessarily:


Shell Wall Thickness: 0.8 mm
Wall Line Count: 3
Alternate Extra Wall: True


Also, I've found it important to print a skirt (perhaps a double-walled one), and watch the first-layer closely and be willing to push more material through and restart: The material in the hotend can easily form a partial clog while the printer runs through its auto-leveling / head-cleaning routine, thus needing to have more material pushed through before the job starts in earnest.

By the way, the model is https://www.thingiverse.com/thing:1993747, by Holodrio on Thingiverse.