Did you tried Intel.com website, might be have driver.. Some newer board may not work for Windows 7.. So, keep in mind, But double check at Intel.com website..
Those newer Cannonlake PCH based chipsets do not have Windows 7 drivers available for them yet, or possibly ever. This is being discussed on the Win Raid forums as well under the Windows 7 USB repository thread. Z370 works because it is a Kaby Lake chipset with its USB drivers working with Windows 7 as they are the same as Z270's. But yeah, those you listed are the Cannonlake ones. Supposedly H310 is possibly Kaby Lake PCH based like the Z370, but not sure. All of the other ones are definitely needing Cannonlake USB drivers though.
I try it too on my HP Prodesk 400 G5 ( B360 mobo ) using USB on PCIE Card. I can install windows on HDD but when time to create new user, my keyboard and mouse didn't work neither in USB on board and USB on PCIE Card. I heard that intel thinking to release B360 USB driver for windows 7. So i only can wait for IT.
Yep, i had the same problems. Intel is/has released the H310C chipset which they officially support w7.