Peter did not say many things here...he did not say we must be born from above either, but we both agree that is needful.
It is what he did say that completely and utterly repudiates the very heart of your interpretation of his words. What he denies to be the antitype of the figure baptism you assert, and what he explicitly identifies as the antitype to baptism you deny. He says the literal antitype where by baptism saves is "by the resurrection of Jesus Christ" NOT "by the baptism in the Spirit" as your interpretation demands.