Is there a way to specify an API version of a call to @RestResource?

Question

I would like to specify an API version when I call a @RestResource via an API. Is that possible?

Why

For some reason, our Spring '19 sandbox is having a weird issue, and I'd like to fix this before production becomes Spring. We put in a support ticket, but I wonder if someone else has hit this issue and solved it, or if it's a known issue that will be fixed before release.

We have enabled Enterprise Territory Management in our org, and we have a class MyRestResource that references UserTerritory2Association. MyRestResource is a @RestResource. When we hit the resource in a unit test, it works just fine, but when we hit it via REST API, it fails.

This works in Winter '19, but not in Spring '19 sandbox.

Here's a minimally-viable failure of this test.

@RestResource(urlMapping='/my-resource')
global class MyRestResource {
  @HttpPost
  global static void doIt() {
    UserTerritory2Association assoc = null;
  }
}

Here's a similar issue:

(Which version of a managed package @RestResource class is used to handle a REST request?)