Using literal hermeneutics it is indeed a fool's errand as mentioned by curiousdannii. There is no reason to expect post flood geography to look anything like pre-flood geography.
If instead you turn to the hermeneutics of sensus plenior (SP), then all the scriptures speak of Christ, and if we miss him, we miss the intention of the author; God.
In SP, the number 4 relates to the word of God as revealed through the four offices or voices of prophet, priest, king and judge. Since it must always relate according to the hermeneutic, we pencil it in to solve the mystery.
We will collect enough clues to see if the rule is showing signs of being completed.
Pison comes from the root פושׁ 'spread scatter' this is associated with judgement.
Havilah means circle, as in teh circle that is harvested in a field representing Israel, and the corners the Gentiles.
Bdellium is בדלח bᵉdolach separation which looks like more judgement.
Onyx שׁהם shoham hints at made equal שׁה through the finished works of the son ם. This might apply to the work of the priest , or the final result of the judge.
Stone אבן ‘eben father אב -son בן and it is the stone (father-son) which is separated at the judgement of the cross.
We might pencil in that the first as the judge.
גיחון Giychown bursting forth is the place where Solomon was coronated as king. Let's pencil it as king.
חדקל Chiddeqel rapid The prophecy is often related as the messiah coming quickly to his people. Let's pencil this as the prophet.
This leaves the last פרת Pᵉrath fruitfulness as the priest. Since Christ died desolate, but was fruitful in resurrection, and he only became a priest in resurrection, we pencil this in as priest.
In SP water is the word of God.
So the tentative picture is that from the beginning God has revealed himself through his word spoken in four voices which are profitable for doctrine (prophet), correction (priest), reproof (judge), and training in righteousness (king).
For those who do not subscribe to SP, it is no big deal, the picture is the same as found elsewhere. For those who do, it contributes to the many themes and patterns found in the mystery which has been hidden from the beginning and is now revealed in Christ Jesus.
Please note that this is not free-for-all allegory. The meaning is teased out of the words and cross-linked with the same symbols used elsewhere.