Hey Gregory L., thanks for the writeup. Confirming what you found: there's no parameter in the current POST /v1.0/generations schema that controls the first card's layout separately from the rest of the document. The only first-card-specific option today is cardOptions.headerFooter.hideFromFirstCard, which only affects headers and footers. So a firstCardLayout or suppressCoverLayout option would be a new feature.
I've also shared your post with members of the API team to see if they have any additional thoughts or suggestions. I don't have a timeline or a decision to give you yet, but I'll follow up here if I hear back.
You could probably pitch for it in Ideas & Requests in Slack here, and if you'd like it tracked publicly as well, feature requests for the API are also collected on the Feature Requests board.