How to get jobs as a Production Accounting Clerk, without many connections to the department?

Hello! I am a Program Director at the non-profit Brooklyn Workforce Innovations in NYC, helping those with barriers to employment get work in the production industry. Our program to train and place Production Assistants has been around for almost 20 years and has been successful.
We launched a Production Accounting Clerk training this year (after hearing from accountants that they were needed). The class was taught by a Key Accountant in local 161. After training, we assist with job placement for 2 years, but we've hit a wall when it comes to finding the right people to hire clerks. Pre-production seems like a whole new ball game for finding work. We have spoken to a handful of accountants, viewed recommended job boards (FB groups and Emily Rice's The List), and attempted to reach out to contacts in a few payroll companies. Most posted jobs are for Accountants in various capacities, but not many clerk positions.

How did you get your start as a clerk (without connections to someone already in that field) and do you have more recommendations?
We have dedicated and trained clerks ready to work, where can I lead them to find more jobs in that department?

Thank you!!