The grey area you are referencing is based on the theme’s CSS code around line 1647
.has-header-image.twentyseventeen-front-page .custom-header,
.has-header-video.twentyseventeen-front-page .custom-header,
.has-header-image.home.blog .custom-header,
.has-header-video.home.blog .custom-header {
display: table;
height: 300px;
height: 75vh;
width: 100%;
}
That controls the height of the .custom-header container, where the height 75vh is the height of the viewing screen (75% of the height). The fallback height is 300px. You will need to play around with the values like I did here (just a very rough estimate) and commented out the vh height and changed 300px to 220px (approx height of your image when it shrinks down in height.
.has-header-image.twentyseventeen-front-page .custom-header,
.has-header-video.twentyseventeen-front-page .custom-header,
.has-header-image.home.blog .custom-header,
.has-header-video.home.blog .custom-header {
display: table;
height: 220px;
/* height: 75vh; */
width: 100%;
}
The problem is that you will have to change the code values for height in the media queries as well for various screen sizes. The one posted above is for small mobile viewing such as a phone.
Going to be a tricky job to do this because of what you are wanting done with the header image. Perhaps take out the superimposed block with text off the image being as you already have that info in the branding container (title, etc).