Ciao,
one elegant solution would be to better controlling exactly what you want to show in landscape and portrait mode. If you want to be responsive with a landscape image on a portrait screen you necessarily have to "lose something", as per @salff comment
My snippet for being more flexible depending on user screen:
<!DOCTYPE html>
<html>
<head>
<meta name="viewport" content="width=device-width, initial-scale=1">
<style>
html
{
background:url("https://www.hotelmedici.com/images/slide_home/11_Fori_imperiali_1600X917.jpg") no-repeat center center fixed;
background-size: cover;
width: 100%;
}
#warning-message { display: none; }
@media only screen and (orientation:portrait)
{
#wrapper { display:none; }
#warning-message { display:block; color: white;}
html
{
background:url("https://s3files.core77.com/blog/images/2013/11/ESB-HalloweenLightShow-1.jpg") no-repeat center center fixed;
background-size: cover;
height: 100%;
}
}
</style>
</head>
<body>
<div id="wrapper">
<h2>Responsive Images</h2>
<p>If you want the image to scale both up and down on responsiveness, set the CSS width property to 100% and height to auto.</p>
<p>Resize the browser window to see the effect.</p>
</div>
<div id="warning-message">
this website is only viewable in landscape mode
</div>
</body>
</html>
NOTE: the code was produced crossing and tweaking your code, w3schools snippet and this answer
Hope this helps, enjoy the weekend,
Antonino