LinkedIn (shockingly and sadly!) only use official partners from http://embed.ly/providers for 'projects' on your profile. Open Graph only works on the LinkedIn feed/sharing updates area.
Otherwise, you can upload an assortment of filetypes to feature, but no way to explicitly to tell LinkedIn which image to use on the profile.
Embed.ly does pick up open graph information on your site, but they don't prioritize the OG information. In fact, Embed.ly wrote a blog post that essentially scoffs at the widespread use of Open Graph tags for sharing and how users and large websites supposedly can't trust them.
EDIT:
To answer the comment:
You can reshuffle things on embed.ly, for example, by disabling your background-image
while you add your website to your profile, or switching your background-image
to the desired one just long enough for you to get the desired effect on LinkedIn. This isn't a guaranteed fix as LinkedIn may recache the project at a later (any!) time which will set it back to your background-image
.