The issue may not be so much one of chronology, but of interpretation/understanding of the Hebrew mindset.
The word "son" (Hebrew: ben/בֶּן) in Hebrew can mean the same as "descendant" as well. It does not apply only to single-generation children. This cultural aspect continues throughout the Bible, and is seen in Jesus being called "the son of David" and David being "the son of Abraham."
The book of the generation of Jesus Christ, the son of David, the son
of Abraham. (Matthew 1:1, KJV)
Joseph, too, is a "son of David," according to the angel:
But while he thought on these things, behold, the angel of the LORD
appeared unto him in a dream, saying, Joseph, thou son of David, fear
not to take unto thee Mary thy wife: for that which is conceived in
her is of the Holy Ghost. (Matthew 1:20, KJV)
Obviously, then, we cannot tell how many generations had passed, but that more than one Phinehas must be represented appears clear, seeing as these two men are presumably several centuries apart in time.
More than One Phinehas
- The first mention of a Phinehas (son of Eleazar):
And Eleazar Aaron's son took him one of the daughters of Putiel to
wife; and she bare him Phinehas: these are the heads of the fathers of
the Levites according to their families. (Exodus 6:25, KJV)
- Another mention of a Phinehas (son of Eli):
And this man went up out of his city yearly to worship and to
sacrifice unto the LORD of hosts in Shiloh. And the two sons of Eli,
Hophni and Phinehas, the priests of the LORD, were there. (1 Samuel
1:3, KJV)
- Yet another Phinehas (father of Eleazar):
Now on the fourth day was the silver and the gold and the vessels
weighed in the house of our God by the hand of Meremoth the son of
Uriah the priest; and with him was Eleazar the son of Phinehas; and
with them was Jozabad the son of Jeshua, and Noadiah the son of
Binnui, Levites; (Ezra 8:33, KJV)
It would be perfectly definitive, of course, if one were able to demonstrate that Phinehas was an adult at the time of the Exodus, for all adults (those aged 20 or above) died in the wilderness except for Caleb and Joshua. This is, however, uncertain; and Phinehas is mentioned as entering Canaan (see Joshua 22:31-32). Therefore, we have only the chronology to follow to understand that the Phinehas of the era of the Benjamite war cannot have been the same Phinehas who was the first-generation son of Eleazar. He would, however, have been of that lineage.
Assuming the most optimal of age ranges, that Eleazar's son Phinehas was barely born at the time of the Exodus, and therefore 40
upon entry to Canaan, he would have been at least 60 at the death of Joshua. Caleb also lived awhile in Canaan, but his younger brother Othniel lived at least half a century beyond the time of Joshua and Caleb there, according to Judges 3:8-11, so at least 70 years in Canaan. Putting just this 70 and the 40 at entry, and we have already 110 years. That was a good average lifetime in those days for one who was long-lived, like Joshua, who lived to be 110. But then we add 18 years for Eglon (vs. 18), and then 80 years following Ehud (vs. 30). All of this took place well before the war with the Benjamites. Anyone living in excess of two centuries would certainly have been notable in those days, yet not a mention of this is made.
Conclusion
The writer assumed readers would know from the time gap that the two individuals named "Phinehas" were not in fact the same person, the son of Eleazar, grandson of Aaron. But that they were both of that lineage is understood. As is often the case today, names, especially good ones (of honorable people) frequently got reused.