Maybe too late, but I noticed the same problem today and looked online for a solution. Didn’t find it, saw you stranded, so I came up with my own fix.
I use a responsive theme, with media queries to switch to mobile layouts. So what I did was inspect the DIV that slides out when using the mobile width, and added this to the right section in the media queries CSS:
.nrelate.nrelate_animate_style_nyt {
display: none !important;
}
So basically what it does is hide the flyout only when using the constrained, mobile dimensions.
It’s working on my site, so check it out if it helps to do so:
https://www.muripo.com/2013/05/08/ramen-burger-sandwiches-crunchy-noodles-between-buns-theyve-gone-mad/