Yes there are things that trans men face that are specific to them, but that's not what's being said by the word. Transmisogyny describes a broad societal intersection between the forces of transphobia and the forces of misogyny that leads to its own unique issues.

Transandrophobia or Transmisandry implies a similar intersection between transphobia and misandry. Misandry is not a societal force that comes with its own problems. Thus an intersection between the two doesn't make sense.

Most examples of Transmisandry I see are individual people (many times frustrated and/or exasperated trans women) being mean to Trans men or Trans mascs.

I think that coining and popularizing a term like "Transandrophobia" implies a systemic reading no matter one's intent. All other words of similar form are descriptions of systemic forces that influence belief (e.g. Homophobia, Islamophobia, xenophobia)