I use uBlock Origin to completely block out the news feed and messaging, and it makes my LinkedIn experience orders of magnitude better. When I visit linkedin.com, now, I'm greeted with a navigation header bar and a blank page where the news feed used to be. It's perfect.
I personally found messaging to not be very useful or relevant, and I just couldn't keep up with the backlog of messages. If they really want to contact me, they can just email me.
Here are the UBO rules:
www.linkedin.com###voyager-feed
www.linkedin.com###messaging
www.linkedin.com##.msg-overlay-bubble-header
www.linkedin.com##.msg-overlay-list-bubble__content--scrollable.msg-overlay-list-bubble__content
www.linkedin.com###msg-overlay
www.linkedin.com###messaging-nav-item