Final update here; it turns out all of these issues are related to a single underlying issue related to the way test portal scoping functions. Right now, test portals do not automatically have access to Sales Pro, meaning they don't haven access to Products/Pipelines out-of-the-box. Apologies for the delay in identification here, there were a lot of red herrings.
That said, the team is working on a permanent fix now In the interim, I can give your test portals temporary access to Sales Pro in order to test these APIs. Each test portal will have 2 months of Sales Pro access, after which time it will expire. This should be enough time for everyone to test the relevant APIs while we continue to work on a longer term solution. I've already given access to the following portals:
The following portals were included, but are not test portals, so I'm unable to give free Sales Pro access. For production portals, access to a particular API is contingent upon the portal having legitimate access to the tool. This means the following portals would need paid Sales Pro access in order to access the Products API. If the folks who own these portals can give me a test portal Hub ID, I can grant access to a test portal:
If anyone else is working on an integration and needs access to test these Sales Pro - related APIs, feel free to comment with the Hub ID of your test portal. I'll continue to update this particular comment as I give access to test portals.