Is there a method to explicitly set Embedded Data on a feedback form from a front-end application?

TLDR:
I need to add user-specific Embedded Data to our form on each page load.
I've spoken with support and we have a way to do it by putting properties on the window object.
It's hard to believe that there is no method exposed to set dynamic embedded data to a given survey from a front-end application.
It's also hard to believe that there is no technical documentation for any of this.
Has anybody else run into this?

For Context:
I am implementing embedded data for website feedback in our application and have learned about the 4 methods to add it via an implementing application:

Cookies -- constrained to singe-value cookies
Value from JavaScript
Events
HTML elements

We ended up going with 'Value from JavaScript'. In the Qualtrics documentation*, it reads:
> Value from JavaScript: This option captures custom Java from your site. The specified value needs to be a JavaScript expression/call.

I spent an hour on the phone with two support people from Qualtrics to find out what they really means is that you need to add a property to the window object that is then mapped to embedded data you define in a Qualtrics Creative.

I, along with every colleague I've spoken to about this, am very surprised that there is no way to do this via an exposed Qualtrics method from a front-end application. Has anybody else run into this issue? Is there a method I haven't found, or are we stuck with adding properties on the window object every time we want new Embedded Data? Is there any documentation for Qualtrics front-end interfaces?

\\* https://www.qualtrics.com/support/website-app-feedback/intercepts-tab/edit-intercept-section/action-set-options/embedded-data-website-app-feedback/