One thing that I think is very difficult to do in your position is to determine what benefits others and what does not. However, I think you're wrong here to be trying to defend this as 'correct', because it's not—or at least the spec doesn't support what you're doing. You should be proudly saying 'this is what I can build out of the most basic building blocks available in HTML. It's as semantic as possible, but there are some tweaks needed to enable particular high value features'.
Ultimately a lot of the modern web trends don't fit perfectly into the HTML5 syntax, and cards particularly are one. They're not 'articles' because they're not 'complete, or self-contained, composition[s]'. They're not 'asides' because they're not 'tangentially related' - although callout boxes I agree are. They could potentially be considered 'sections' although I'm not sure you would list individual cards explicitly in a document's outline - plus from a technical perspective how do you differentiate a 'section' card from any other type of section.
I think it's important to understand that there's no way to make everyone happy here, and there simply isn't a good semantic way to create cards using the tags that exist. I think in most cases, cards are a presentation of an item of sorts (perhaps even a 'list' item?) but HTML doesn't have a simple 'item' tag, and the spec warns that although headings are valid inside li tags, it's probably not correct semantically.
Key is, there will be some people this helps. There will be some it doesn't. For every (completely valid) concern that people (including myself) are raising, the only fix is to add more complexity, which makes it less easy to use.
FWIW, I think you've done a great job building something usable and useful, thank you.