1.
Jewish proselyte baptism. I believe so called Jewish proselyte baptism is a post-exilic (and likely post AD70) development within Judaism. There is no Biblical example or hint of proselyte baptism.
2.
John's baptism. John's baptism was not directed at gentiles, therefore was not "Jewish proselyte baptism". It was a new thing, as evidenced by the theological dilemma it posed: who are you be baptizing if not the Christ, that Prophet, or Elijah?
3.
Baptism vs mikvah. Both John's baptism and Christian baptism required two participants: the baptizee, and the baptizer. Jewish mikvah requires only one participant: the one being immersed. Both John's baptism and Christian baptism were non-repeatable, that is, a person received it once and there was no provision for it to be repeated. Mikvah is repeatable.
4.
Baptismal formulae. Regardless of what one believes the proper formula to be, that there IS a formula of some sort is demonstrated by the following: A) History records the early introduction of controversy surrounding the proper baptismal formula, but there is no record of an innovative introduction of a formula per se. In other words, if original baptism did not involve the baptiser using a formula at all, we would expect to be able to identify when such an innovation was brought in. We can't, and the record of baptismal controversy simply assumes a formula of some sort was always used. B) The presence of both a baptizee and a baptizer implies the use of a formula or stated declaration of intent and purpose on the part of the baptizer.
Matthew 28:19 is a command to the baptizers, whereas
Acts 2:38 is a command to the baptizees. Thus, BOTH are commanded to "do something in the name". If
Acts 2:38 is a command for the baptizee to verbally invoke the name in baptism, then
Matthew 28:19 is a command for the baptizer to do the same when baptizing. This is further indicated by
James 2:7 which can be read as "that worthy name which was called upon/over you". Additionally, the priestly blessing illustrates the same principle of placing the Name upon a people via oral invocation of that Name by the representative of that Name.
Now, as far as the mechanics, Scripture gives certain directions that are essential elements, while remaining silent regarding certain other directions which therefore are accidental elements and subject to local usage. For example, two persons, water, immersion, faithful profession of faith, are essential elements. Nose held or not, forward or backward, arms crossed or not, water temperature, stream, pond, lake, ocean or bathtub, etc are all accidental elements that are up to the church, minister, or individual to decide. The same applies to the express words used in baptism: as long as the essential element of "in the name of Jesus" is included, without adding names, or otherwise subverting the intention and purpose and object of baptism, then the particular form of words is flexible. The same principle holds true in benedictions or Eucharistic prayers: as long as the essential element of thanks to God through Christ is preserved and centermost, the one praying can use whatever words they want.
As for Bible vs Bible interpretation, one might say EVERYTHING is interpretation. The question is, which interpretation is most faithful to the Biblical data? Is affusion more faithful to the Biblical data than immersion? Etc. But this gets into the question of epistemology which is beyond the scope of this thread, I think.