Emphasis & Addition: さえ vs すら vs ばかりか vs はおろか
The key split is between plain addition (ばかりか: "not only A but also B") and a difficulty chain (はおろか: "forget A — he can't even do B", where B is the easier thing).
The patterns
こそ
it is precisely ~ (emphatic focus)
今度こそ、成功させたい。
This time for sure, I want to make it work.
さえ／すら
even (one extreme example)
彼は自分の名前さえ忘れてしまうほど疲れていた。
He was so tired he even forgot his own name.
ばかりか
not only ~ but also (plain escalation, positive predicate)
彼女は英語ばかりか、フランス語も話せる。
She speaks not only English but French too.
はおろか
let alone ~ ; can't even do the easier thing (negative predicate)
彼は漢字はおろか、自分の名前もひらがなで書けない。
Forget kanji — he can't even write his own name in hiragana.
Decision procedure
Is the sentence "A, and also B (negative)" where A is harder than B?
Commonly confused
さえ vs すら
Functionally the same "even". すら is the more literary/heavier register. You do not need to agonise over which is "correct" — read either as "even".
はおろか vs どころか
Both express strong contrast, but どころか is a *reversal* ("far from warm — it was scorching"), while はおろか is a *descending difficulty chain* and almost only appears with negative predicates.