You are raising a rather large number of issues here.  It is hard for me to address all of them in a short reply, but let me make at least some progress.

First of all, you say that both sides can argue that there is archaeological evidence in support of their scriptures, and that this more or less cancels out–in other words that archaeological evidence is not helpful in “proving” either the reliability of the Bible or of the Hindu scriptures.  I disagree with this.  First of all, there is little if any historical content in the Hindu Scriptures.  In other words, little if any of the Hindu scripture is of an historical nature, and therefore archaeology can neither support nor deny Hinduism.  There is NO archaeological evidence which supports the reality of Krishna.  None.  We do not know when he supposedly lived.  Nor do we know where he supposedly lived.  Any attempts to change this involve speculation.  Let me repeat.  There is NO archaeological evidence that an unbiased person would say supports the reality of the god-man mythical person known as Krishna.  The case with the Bible is clearly hugely different.  We have the Tel Dan Inscription, found in the city of Dan, which mentions the names of David, Jehoshaphat and other actual kings who actuallly lived.  We have the Taylor Prism, which has an actual inscription of the actual king Jehu.  The Old Testament is immersed in history, with literally dozens of locations which have been excavated, and a number of persons named who are know to both history and archaeology.  Archaeology does not “prove” the Old Testament, but it quite strongly supports its reliability.  Anyone who says this about the Hindu scriptures (Vedas, Upanishads, Gita, etc.) are simply speaking falsely.

About reincarnation, most Hindus believe that all humans have been through repeated cycles of birth, death and reincarnation.  Perhaps dozens, perhaps hundreds of lives.  Yet, population experts believe that upwards of 25% of all humans who have ever lived are alive at this moment.  This fact alone makes the proposal that all humans go through many cycles of reincarnation insupportable.  Of course, there is no hard evidence for reincarnation, although some have made some rather interesting anecdotal claims of individual reincarnations.  Such evidence will always be debatable at best.  However, we need to admit that it is difficult to outright disprove reincarnation.  It is difficult to prove that it has not happened. It is hard to prove a negative.  So, in the end, although the population numbers seem to make the idea of dozens of cycles of birth, death and reincarnation seem absurd, it will come down to whether we believe the authority of the scriptures which propose that reincarnation does exist (Hinduism, Buddhism, Jainism) or the scriptures which claim that it does not (the Bible).  I believe that the evidence for biblical inspiration is overwhelming and that the case for inspiration of the Vedas or the Hindu epics is nonexistent, and therefore, I reject reincarnation more based on the authority of the relevant scriptures than on reproducible evidence.

If Hindus say that Jesus was a mythological person, then they are clearly and unambiguously wrong.  Honestly, I have not met such Hindus.  All I have spoken with agree that Jesus was an historical person.  But… If any claim he was a myth, then they are wrong!  They are simply wrong!  We know where Jesus was born, where he lived, when and how and where he died.  We know the names of his mother, his father, his cousin, three of his brothers, and literally dozens of his close friends.  Many of these people are also known from historical documents outside of the Bible, being mentioned by Josephus, the Jewish historian and by others (including the apostle James and James the brother of Jesus, for example, as well as the apostle John).  Here is the bottom line. Krishna is literally and certainly a mythical figure and Jesus without any reasonable doubt is an historical figure.  Anyone who says differently ought to explain their position with actual facts.  Trust me, they will not be able to do so.

One caveat.  It is possible, though not likely, that there was an individual in the distant past about whom we know virtually nothing who served as an historical person around whom the myth of Krishna grew.  I cannot prove that such a figure did not exist.  In other words, there may have been a man who lived, we know not where or when, who said some things and committed some acts which created a story which eventually developed through a long process of myth-making into the Krishna of the Gita or of Mahabharat.  I am not saying that this is the case or that it is not, but only conceding that it is possible.  But if this is true, then we know either literally nothing of this person of any historical value or we know virtually nothing of this person, to the point that it is hopeless to even consider discovering with any precision where or when he lived.  In any case, the Hindu epics are NOT historical accounts of such a person.  In any case, to compare the historical person whose words we have, and whose acts have been recounted by eye-witnesses to this mythical person who probably never lived, but if he did we know nothing factual about him is nonsensical.  You can stand quite firmly on this ground.