Philip F. if you need 'smart' scraping https://www.browse.ai/ is a good option. You can essentially transform your scraping into an API and connect it to clay (by creating a webhook inside make or zapier)
For better accuracy, since most Linkedin page present a website, I would first scrape the website from the company page. Then for those not found use a SERP search with "linkedin.com/company [COMPANYNAME]"
hope that helps