Ahmes' promises are fulfilled in the 2/n table, the EMLR, the Akhmim Wooden Tablet and other texts (Reisner). Ahmes, sadly does not fully disclose his thinking by methods, a point that you have fairly made. However, to jump to the imagination level, your suggestion, and not attempt to read and discuss the common arithmetic elements in the 2/n table (as partly reproduced in the Kahun P.), EMLR and the Akhmim Wooden Tablet, the later reviewed on Wikipedia by:
is continuing Otto N. and Peet's 1920 points of view, throwing they baby (scribal arithmetic and its quotient and exact Egyptian fraction remainders) with the bath water (by only transliterating the hieratic script into hieroglyphic equivalents).
Hieratic script ciphered its numerals, an intellectual leap noticed by Boyer, a large subject that we also need to discuss.