Sounds nice if you can do it, but it also seems to require a deep familiarity with the author that is impossible, short of actually knowing them personally? This is what makes me nervous about anything "Straussian", in most cases it requires a lot of discipline to avoid just filling in gaps with what you yourself wish the author was saying.
Beware, Straussian reading largely means reading a text and making it mean anything you want it to. Your evidence is the “esoteric meaning” you uncovered. The magic of this is when someone tries to debate you using the same source you can retort that your critics just haven’t read close enough or have not grappled with the material the same way you have. Despite being advertised as otherwise it is a rather unscientific method of reading a text and perhaps for this reason it is so prolific among the American right.