Great post, @Dan - Copywriting Course! 

When I tried this, I noticed that LinkedIn doesn't let you edit anything about the feature link image. It seems to just grab the first image in the page body.

That's fine if you control the page or the page has a good image. But, a lot of pages don't have images that look good in the square or are relevant to your CTA.

ABOVE: My homepage gives me my social proof logos. Cool for my site, not so great for LinkedIn.

The Workaround:

If you don't control the page or don't feel like making a new page just for LinkedIn, here's the work around I used. Create a CTA post.

Step 1: Create a new post on LinkedIn.

Step 2: Write your post, but DO NOT include any links. This is important. If you add a link first it removes the option to add a photo.

Step 3: Add a photo to your post.

Important: To make sure the part you want visible is shown in the featured profile section, it should in the middle of your image. A 1:39:1 rectangle to be exact. I made my image square, but on your profile, LinkedIn actually crops it down to a 359x259px size, or a 1.39:1 aspect ratio.

Step 4: Once you have your image, you can add a CTA link and any LinkedIn hashtags.

Step 5: Post your CTA post, and then follow @Dan - Copywriting Course's steps above, but choose "Add a post" instead.

The neat side benefit is that you're including a link AND getting your CTA in front of your existing connections. I have around 200 LinkedIn connections and NEVER post anything. This post got me around 480 impressions.