Frankly, the choice of high resolution ADC was primarily due to my having trouble with PIC programming! I had a program that was very close to what I needed, and I could trigger the MCP3551 to take a measurement and verify that the data was being sent back to the PIC with a logic analyzer, but I just couldn't get the PIC to read the data, and I didn't have the hours of dedicated debug time to find the solution.

Here's a video showing the board I designed in KiCAD to hold a PIC microcontroller and the MCP3551 (as well as various regulators and connectors) along with the HX711 board I am ultimately working with now.

https://www.youtube.com/watch?v=KBpizvyYi9U