To reinforce what others are telling you: find hiring managers that would be interested, by first talking to researchers/engineers that might be interested. Even so, its a numbers game so that your results depend heavily on investing a lot of effort, and positive feedback is sparse. Don't let lack of it discourage you.

Its also strongly affected by the state of the market, which as you said, is not the best. If you are getting low on runway, sometimes there is an easy postdoc to be had in your own org because people know you or your advisor.

I say this because it might be suboptimal to focus on front door recruiting processes. They are designed to detect the easily legible: how well can you code? years of experience? what is your availability? they are not designed at all to see the opportunity in a person's lived experience and how it combines with their skills. Even when a recruiting specialist sees the right thing, they do not generally have the skilled confidence to champion for it.

I might have an idea for you (not exactly what you talked about searching for), but would need to know more about your ML background. If you want, DM me and lets chat.

Wishing you the best in your search!