Since you will use the latter, your version of the argument will already be clearer qua argument. If the author's language is obscure, you can put it in more familiar terms even if it takes more words. State the premises and conclusion in a list or outline, not in regular paragraph prose. Give each premise a number to enable cross-reference and to show structure. Indent to show subordination.
Visual clarity can contribute significantly to logical clarity.
Limit each numbered entry to a single proposition. This will help you and your baffled reader see whether the argument has any gaps or weak links. If one of the propositions you find yourself recording is obscure or controversial, then provide an indented sub-explication for it. Without this, the baffled reader will learn only that the author's argument depends on a certain difficult premise, not what that premise means or why the author thought that we should accept it. Your comments on those premises, or sub-explications of those premises, should be subordinated and indented so that we can skip them when we want to read just the argument itself.