Hi Robert,
I'm a little puzzled by your question. Do you think only the high priest could be a type of Christ? There are lots of different typological connections from the OT to Christ apart from that - for example, Isaac in Genesis 22 and the bronze serpent in Numbers 21, and of course King David. I've argued in an academic essay that Nehemiah was actually one of the best "kings" Judah ever had (in terms of the ways that the Chronicler rates kings). Insofar as he met the standards of a good king (even though he wasn't one himself and may well not have been descended from David), he clearly pointed forward to Christ - and insofar as he was unable to bring about a lasting change in the people (see Neh 13), he clearly showed why someone greater than he must come. As Gordon McConville has suggested, there is an air of "partially realized eschatology" in these post-exilic books: thankfulness for what God has given in the "now" through the Persian authorities but also longing for the much greater vision anticipated in the prophets in the "not yet".