Is there any service where I can describe stock footage that I need using human readable search terms and sentences and send out a search request to multiple footage archives at once, so I will not have to contact each one individually, that will then use real humans or otherwise search intelligently and send me a list of suggested and relevant footage clips?
I don't know what you mean by human readable search terms, as opposed to keywords or tags?
But for a meta search directory service I would recommend (know of)
(If anyone knows of any additional search engine stock video directories, I would love to know about it as well)
Otherwise, ya, you would be going through each service looking for footage.
These are the stock services that I am aware of:
http://www.gettyimages.ca/footage/ <- used by major media outlets
https://www.videocopilot.net/products/ <- geared more to adding effects to clips
And many more... I am sure others can chime in with their favorite sites.
I use VideoHive - large collection of clips and affordable prices.