One trick to evade some of LinkedIn's detection:
A big part of its detection relies on finding known extension resources at URLs of the form `chrome-extension://{extension_id}/{file}`
An extension installed from the Chrome store has the same `extension_id` for every user. But, if you just extract the source for that extension, and then load it yourself, you'll get a NEW extension_id. Same extension with the same functionality, but its extension_id will be completely new so impossible for LinkedIn to query.
Granted this won't evade the second type of detection LinkedIn employs, it'll help you evade quite a bit. I often clone extension source code anyway since it mostly protects me from malicious extension updates (by effectively disabling updates).