Excellent. This all makes sense. One issue I bumped into was that after I got it working (using your DOM selector provided above) it did load the results into the main grid as expected, but it loaded all of our “blog” posts and not any of the posts that the search instance is configured to index. Same search bar works okay when deployed without the archive “live load” functionality, loading the CPT “resources” which is the only one it is configured to display. But when the live load is enabled, it loads standard “blog” posts instead.
I may not go with this use case in the end, so please don’t put too much time to it, but if you have an easy answer for that please let me know so I can continue experimenting.