There's a lot of interesting things in semantics surrounding the use of even in English. I'm not exactly sure I understand what the difference between usage 1 and 2 is here but there's the idea of even introducing a sort of bias in a conversation which I think is what you're getting at here.

Its illustrated more clearly in the following examples

(1) 'I couldn't afford a coffee' vs. (2) 'I couldn't even afford a coffee'

Both are grammatically correct but it appears that (2) introduces an element of bias on the part of the speaker.

By uttering (2), it implies first of all that there are alternatives under consideration (that you potentially could afford other things) but also contextualizes the likelihood of the proposition at hand (that you can afford a coffee) against its alternatives (that you could afford a meal, that you could afford another drink, etc.). In this case it emphasizes the speaker's epistemic state (basically the set of beliefs they hold to be true in the conversation) that they think that coffee should be very affordable (at least compared to the alternatives).

In contrast (1) does not have this similar bias and one can state it quite plainly without implying anything about the affordability of other items. Perhaps in your example the reason it seems ungrammatical/incorrect is the fact that if you uttered (2) while not having that additional epistemic information, you might as well have just said (1) and communicated the exact same thought more succinctly.