Hey @ZacharyStevens - very familiar with the Asana Zapier connector and the bugs it has along with it.
When you refresh the fields and they don't come up, do you by chance have 2 projects listed? Yes, the integration let's you select multiple projects, but when you do, it gets confused as to what custom fields to show, so it doesn't show any.
Another area where we ran I to this was when you're using a custom variable as the project ID. It seems Zapier doesn't recognize the custom ID written even if it's a valid Asana Project ID unless selected specifically from the drop-down.
We use Webhook functionality to connect to Asana all the time now though because of some of these issues. Also, searching for an Asana Task based on custom field value (support ticket 😵 for example, is something we use all the time. You need to use a custom Webhook to accomplish this type of thing though, the Asana Zapier connector is a bit buggy/limited in some of these unique use-cases.
Cheers!