Well taking into your leading and lagging metrics, sharing some of the ways that jas worked for me from my experience:
• In the side banners on blogs- one of the easiest way to get the initial traction to your case study if your receiving good traffic.
• Add a hello bar in all the pages of your website
• Since, it's a case study, it can be repurposed in different content formats (stats, images, infographic from the case study) on social media- like a teaser.
• Add it to the newsletter if at all there is one.
All this would start giving the leading metric almost instantly and sign-ups will start to come in, from the blogs that are transactional intent.