I don’t think step 2 is correct (IE: you can’t use Archives Interface), as the “instead of accessing it” never happens.
For reference, the text in question (my notes in bold):
Whenever you access cards in Archives (1), you may remove 1 card in Archives from the game, instead of accessing it (2).
Archives Interface basically has two abilities (annotated above). When you reach the access cards step of the run, effect (1) puts effect (2) into play, but not immediately resolving, as this effect requires accessing a card, which occurs later (or, in the Eater case, never).
Drawing this conclusion from how SS was described to work back in the days of the SS/CtM war of 2016.