Displacement Measurement. A digital tire tread depth gauge is the lowest cost linear displacement measurement solution that I have found so far. The most important consideration is that it has the required resolution of 10um and minimum range of 12mm. Fortunately, others have already determined how to use an Arduino to log length measurements from these digital gauges -> https://www.instructables.com/Caliper-Data-Interface/. The only real challenge being that these devices use 1.5V logic so a logic level shifter is required. 

Microcontroller. The ESP32 is the obvious choice to meet the low-cost and wireless data transfer requirements of the OpenDendrometer.

Real Time Clock. I have used DS3231 RTC modules in the past for data logging projects with great success. The primary reason for using the DS3231 module is that the ESP32 internal clock is not accurate enough for the month or greater operational period. The second reason is that I will likely be configuring the DS3231 to wake up the ESP32 from long periods in sleep mode in an effort to minimize ESP32 power consumption.