I had the same problem ..... so I made a smaller header that worked well on all pages and used my larger image on the the home (index) page using the parallax image feature and set a ratio for it to scroll. Hope this helps.
Anything that is in the header section will show on all pages, there is not a way to change that. What Fran6251 suggested is exactly correct. I recommend you create a smaller header section with your company name and navigation menu, then you can add a section on each page underneath that for you to create the mock-header with separate images.