Find cards where user X is assigned to checkItem

We need to find a way, using the api, to request cards where a user is assigned to a checkItem, but he’s not assigned to the card.

I found that, using
GET /members/xxyyzz?
{card_checklists: “checkItemsAssigned”, card_checklist_checkItems: “assigned”, cards: “checkItemsAssigned”}

I get these results in the “cards” property.
But, if I have thousands of these, is there another method to query just cards, with paging?

If we could use the “filter” property…

Or, if I can do this using the “search” endpoint, with a special query, that would be nice.