Matthew is a later version of the Gospel of the Hebrews used by the Ebionites
"In general, scholarly opinion has been, and continues to be, that the Gospel of the Ebionites is either an indiscriminate harmony of the Synoptics or a corruption of the Gospel of Matthew."
Edwards, J. R. (2002). The Gospel of the Ebionites and the Gospel of Luke. New Testament Studies, 48(04), 568-586.
The author naturally qualifies his statement because he is arguing that the fragments preserved by Epiphanius show that the Ebionite "gospel" used Luke as a main source. As for the gospel of the Hebrews, not only do we have a handful of quotations that make up the entirety of the extant text, but it is associated with the "Nazareans".
I'm wondering how there could be evidence (let alone what it is) demonstrating that Matthew relied on a "gospel" that survives in a few lines, let alone that this is also the "gospel" used by the Ebionites (another text which barely survives related to a group we known next to nothing about).
John's anonymous, but my educated guess would be Ignatius or Polycarp. John is pretty gnostic.
It is fairly certain that John wasn't written by one person (apart from anything else, the authors tell us that they are relating the teachings of the beloved disciple and that "we know that his testimony is true"). The literature on the Johannine community is vast, but interestingly the oldest extant fragment of the NT is from the first half of the 2nd century (~125 CE) and it is from John. It could be that both of those you mention were involved in writing John, but it seems to me to be quite speculative to begin with and all evidence (e.g., comparisons between the language of John vs. either of the authors you mention) tells against it.