You could delete your linkedin account
You then move them way down in your list of admired companies and actively badmouth them whenever it's appropriate - with the long term goal that this information will spread, hopefully ruining the value of being on the network to the point where it is no longer a useful resource and THEN delete your profile.
That's what I'm going to do.
However, LinkedIn contains a great deal of discovery and connection with people you don't know- if you removed your work history etc. then the site isn't going to be as much use to you. It isn't anywhere near as easy.
I registered a new email at a disposable email address and set that as my main email while deleting the rest.
After that I changed some keydata in my profile to things that are incorrect and waved goodbye linkedin.