If the criteria for blog selection does not change very often, you could save a list of qualifying blogs in one arbitrary place like the main site’s options table. From other blogs, you would need to switch to the main site, get the list, then switch back. Somewhat better than switching to every blog in existence to get one bit of data from each. But keeping that one location list current if the criteria is always changing would be a PITA.

Is your site sub-domain based or sub-directory? If sub-directory, you could maybe use the sitemeta table if it has each blog’s sub-directory listed there. On my sub-domain site, that table only has one site entry and multiple blog table entries. I suspect sub-directory sites may be the other way around, but IDK.