You might start by taking to your presbytery E & S committee and asking their help.

Curious about why you don't want to "just throw your name in the hat next winter?"  As someone who supervises regularly - 5 students in the past 4 years - part of both the challenge and richness of internship is the element of the unexpected in the matching process.  Interns get challenged in ways they don't expect to be challenged during internships and everyone involved in the process learns from the good, the bad and the ugly...or at least, we hope they do.

Jim Lochhead

I'm assuming that you are in the national 8 month internship stream; that's not a safe assumption with several other streams available these days - AST's in-community ordination stream (doesn't have "internships"); St. Stephen's (calls it a residency, I think); Candidacy Pathways program (just getting started)...

Hello em-dash and welcome to WonderCafe.ca

I would second DKS' suggestion of connecting with your Presbytery E&S.  That is, without a doubt the best way to start.

jmlochhead also points out that there are a variety of streams in which the supervised education component can be met.  Not knowing which stream you belong to I am not sure which route is going to offer you the best opportunity to learn.

So, checking in with Presbytery E&S seems the most prudent way of getting started.

Grace and peace to you.

John