It is debateable whether "epignosis" means "accurate" knowledge. We know for sure that it is an intensive form of "gnosis" - knowledge - because of the "epi" prefix. But what does this prefix indicate?
Most lexigographers believe that whereas "gnosis" simply means "knowledge" in the intellectual grasp of factual information, "epi-gnosis" would indicate a fuller understanding of its moral or ethical demands. Indeed, the word is used, in its twenty occurrences in the NT, only to the relationship that "epi-gnosis" has of spiritual matters.
For instance, believers need the "epi-gnosis" of the Son [Eph 4:13], the "epignosis" of the Will of God [Phil 1:9, Col 1:19, etc] and the "epi-gnosis" of the mystery that is Christ Himself [Col 2:2, 2Pet 1:8, 2:20]. There is also the possibility of being an absence of "epi-gnosis" when it comes to God [Ro 1:28]. The Israelites had, according to Paul, a zeal for God, but this was not based on "epi-gnosis".
There is also the possibility of having an "epi-gnosis" of sin [Ro 3:20] and of The Truth [1 Tim 2:4 etc]
Just as Mum [you from Aussie?] is aware of the tautology of saying "accurate knowledge", most lexicons will define "epi-gnosis" as "full" knowledge, or "complete" knowledge. The emphasis then, is on its totality rather than its accuracy.
One can have less than complete knowledge of God, which could lead to a missapplied zeal for God as in the case of the first century Jews.
Oddly enough, the NW"T" translators admit this in the use of the verb form of this verb, "epiginosko". Twice they translate this verb as "fully know" [Matt 11:27] and twice as "know fully" [Lu 1:4, Ac 22:24]