Does Joshua leading the faithful across the Jordan parallel life in Christ?
Indeed, not only do the names "Joshua" and "Jesus" equate to what many refer to simply as "Yeshua," but it thus follows that they represent the same meaning: "Yahweh is salvation" (some may differ a bit on that translation).
I. — Before we get to the Jordan "River of Death" we might reflect on Moses and the Egyptian captivity. That is because Israel was metaphorically a "slave of sin (Egypt)", since the land of Egypt was emblematic of "sin and death". Moses was (eventually) able to bring Israel out of Egypt and subsequently saved them through the Red Sea. This is where the entire nation was "baptized" (1 Cor. 10:2). They had obviously heard the Word of God, and believed it. Their repentance was demonstrated by their abandonment of Egypt (sin) by following Moses (who typified Christ).
II. — The Israelites were then "tested" for 40 years in the wilderness. This, I believe, symbolized the trials we face in our newfound faith. Unfortunately, due to their persistent rebellion against Moses, most of the Jews that emerged from Egypt died in this forsaken wilderness. We too can do precisely the same if we abandon our faith and obedience to God, only to return to "Egypt" through sinful behavior.
Once in this desolate no-man's land, Moses became emblematic of the Law: He was the Law as an agent of God. And, because much of the nation eventually did obey Moses (after many trials and punishments), Israel might be viewed as "the body of Moses" — just as Christians are "the body of Christ." (This prompts another discussion for another day.)
III. — When the time came for Israel to begin preparation for the Promised Land of Canaan, Moses then sinned against the Lord. While his sin might be viewed as rather trivial, that is "striking a rock instead of speaking to it" (Num. 20:11-12), this may be a lesson for us that there are no "trivial sins" before the Almighty.
However, there may be a much greater truth here if we are prepared to look for it. The Law, by itself, could never save anyone. It is the means by which we recognize that we have violated, or transgressed God's commandments (1 Jn. 3:4, when we do). Merely obeying the Law of Moses offered little relief, just as when we obey the speed limit, we never expect to be congratulated for it.
This, I believe, is why Moses (the Law) could never enter the Promised Land. Here, it would take someone like Joshua, Yeshua, to deliver, to fulfill the Promise. That "promise" was the gift of the Promised Land.
IV. — When Joshua, another type of Christ, was chosen by God and Moses to lead the new generation of Israel into Canaan, they first had to cross the Jordan "River of Death." This would be the "baptism" of these new people of God, those who had not yet been circumcised (only those who died in the wilderness had been: Josh. 5:2-7).
As stated in the OP, yes, "the Jordan River has traditionally been characterized as the 'River of Death.'" Indeed, Joshua then led the people through this river as it was overflowing* — an intimidating sight to behold. They did so as they walked across the dried lakebed (as the priest's feet touched the water) just as with Moses and the Red Sea.
We should not miss the parallels here: Jesus, Yeshua, now leads his people across their own "river of death", that is, physical death — into the promised land of heaven.
V. — This is hardly coincidental. We might even extend the symbolism further. The first enemy the Israelites were to conquer, once across the Jordan, was the city of Jericho. Here, we might observe another passage of relevance. As the walls of Jericho fell, the priest were to blow their trumpets and the people were instructed to shout:
Joshua 6:16b: “Shout! For the LORD has given you the city."
VI. — Just as Joshua commanded the Jews to "blow their trumpets" and "shout for the city had been given to them" by the Lord, we too will be given a city: the New Jerusalem of Heaven! Note how this is described in the Book of Revelation:
Revelation 21:10-11: "And [the angel carried John] away in the Spirit to a great and high mountain, and showed [him] the holy city, Jerusalem, coming down out of heaven from God, having the glory of God."
The symbolism of Joshua (and Moses) could not be more pronounced.