But LinkedIn as of this morning has updated their public profile policy to make it difficult for vendors like us to get access to this data, even though they continue to sell the job change information to their customers (based on how each person updates LinkedIn job status): https://www.linkedin.com/help/linkedin/answer/a518980
Historically there was a fine balance.. LinkedIn collects data from its users by telling them that they will not sell their data and they make money through making connections (LinkedIn recruiter / sales navigator).
Data providers would rely on publicly available information to update their records so that sales teams can prospect target accounts accurately.
Any thoughts on how we fight this battle?
Go into a different line of business.
Your business model is entirely dependent on free-riding on another company. LinkedIn has had anti-data scraping policies for over a decade, your business is not special, and you are PUTTING YOUR CUSTOMERS AT RISK by trying to knowingly find workarounds to LinkedIn's terms and conditions.
Use your creative energy to find other, better ways of providing value-add for sales teams. Automating something that should only take them a few seconds to do on their own is not actually improving the sales process - you are only helping them automate very, very low quality sales motions.