Magnum, I agree with most of what you say except that I have always understood "accurate knowledge" of the truth or the Bible or whatever to be in contrast to a superficial or incomplete knowledge of the same. In 1Timothy 2:4 Paul is saying more than that it is God's will people should know (gnosis) the truth. He is saying, as you expressed it, that they should have a full or complete or thorough or intimate knowledge of truth.
In Thayer's Greek Lexicon it describes epignosis as "precise and correct knowledge" which is scarcely different to "accurate knowledge".
The word is found at Romans 1:28; 3:10; 10:2; Ephesians 1:17; 4:13; Phillipians 1:9; Colossians 1:9, 10; 2:2; 3:10; 1 Timothy 2:4; 2 Timothy 2:25; 3:7; Titus 1:1; Philemon 6; Hebrews 10:26; 2 Peter 1:2, 3, 8; 2:20.
It may be helpful to review how it is used in these scriptures. It is used in the LXX as well.
In my opinion when epignosis is used of God and Christ then "intimate knowledge" would probably be more appropriate, but when used of something abstract, like truth, "accurate knowledge" is true to the sense of the word.