I was not aware of the current rewards system, but that then raises the question of why the zine I linked didn't use it? Were they aware of the capability?
Looking at the documentation for rewards, it seems similar to the Kickstarter system (correct me if I am wrong here). The kickstarter system works almost opposite to Bandcamp's way, in that you purchase a game in order to receive a hardgood, while for bandcamp you purchase a hardgood and receive a free softgood. While in practice they are similar, for a userbase the verbiage could imply that the use cases are different (and thus not supported). More verbiage throughout the site (especially during onboarding new users) that they can actually sell hardgoods via itch would also encourage sellers to make product.
A feature I would love (and am very disappointed that bandcamp does not have) is being able to filter a search for sellers with hardgoods in stock. Maybe this would solve the visibility of the capability?
As far as improvements to the flow goes, I haven't personally tried it but I will make an effort to within the next two weeks. It does not sound like you have a shipping label generator; I think that would be a huge benefit to the website for hardgoods! A possible implementation would be an initial design of the label written in html and css, and have it sit in an AWS lambda function. Then populate the values and have Phantomjs take a snapshot and return a PDF to the user for download. I've used this flow before and it is probably the best way to provide web generated content to a user that consistently prints well, and you can have the server perform this flow at any time without needing user interaction.
An easier implementation would be just have a web page with print css that the user clicks to, but cross browser testing is a bitch for this and it requires that the user goes to the page and uses their browser's print feature in order for it to be generated.
edit: also, bandcamp has a nice "why sell merch with us" page that explains why it is a good idea for users. Maybe some ideas can be drawn from here for itch.io encouraging users to sell hardgoods?
edit edit: bandcamp supports searching by merch :\ rip wallet