The problem with Vine's definitions (and much more with those who use them without an "accurate knowledge" of NT Greek) is that there is not necessarily a shade of meaning for every prefix, diminutive, particle, or other detail of koinè Greek. The difference may just be stylistic, nor semantic.
Cf. Bultmann's article in Theological Dictionary of the New Testament, vol. I p. 703f:
[epiginôskein] is often used instead of [ginôskein] with no difference in meaning. In Gk. [epignôskein] can mean "to observe" if the prepos. is emphasised, but this means much the same as "to perceive," so that any distinction disappears. In fact the simple and compound forms are used interchangeably in the pap[yrii], where [epiginôskein] really means "to affirm" or "to confirm" rather than "to test," as Preisigke maintains. Only in the sense of "to (re-)cognize," or, in law, "to reach a further conclusion," does the compound have a special sense, but this does not affect early Christian usage, nor do certain special uses in the pap[yrii]. In the LXX the two terms are often used as equivalents, and they occur as par. in Hab. 3:2; cf. Ez. 25:14 with Is. 43:10; Hos. 14:10 with Jer. 3:13; Ps. 78:6 with Ps 86:4. (...)
P. 707:
Rather curiously, the compound [epignôsis] has become almost a technical term for the decisive knowledge of God which is implied in conversion to the Christian faith. (...) To be sure, there is no technical use in R. 1:28 (...). This is plain, however, in the Past[orals]; cf. 1 Tm. 2:4...
It is just as hard to find any strict distinction between [gnôsis] and [epignôsis] in the NT as it is in the LXX and Philo...
And perhaps Bultmann himself is reading too much into the epignôsis of the Pastorals.
IOW a specific, doctrinal, "sectarian" sense of epignôsis may appear only in 2nd century Christianity (the Pastorals and 2 Peter, as well as Patristic literature). In this context it could be better translated as "true knowledge" (which is still wider than "accurate knowledge"). But this cannot be read backwards into 1st century texts, where epignôsis means no more than gnôsis.
