A different thought, the Pro Mini dimensions are 0.7" x 1.3":
https://www.arduino.cc/en/pmwiki.php?n=Main/ArduinoBoardProMini
If you have space for 1.1" x 2.8" (this includes OLED display), then Lolin ESP32 with OLED for <10$ might be an option. That has 160MHz (20/10 times the Pro Mini clock speed, and 32bit CPU), 520KB sram instead of 2KB, is programmable with Arduino IDE and uses standard SSD1306 library for the OLED. So if size and price are no blocker, it may be an alternative for you, see this thread:
https://forum.arduino.cc/index.php?topic=495555.0