My goals overlap a lot.
If you haven't seen https://huntr.co I think they do a great job helping you manage job hunting.
I think the social feed is LinkedIn's weakness as well. It creates a bad incentive for the company. I would use it a lot more if the feed was useful instead of fake engagement bait. Same with LinkedIn Learning being more about basic entry level courses than quality expert content.
My suggestion is to help people build valuable networks that discuss actual hard topics. I've seen a few companies try to create small exclusive groups that cost money to join but they try to guarantee meaningful, intelligent discussions & sharing. LinkedIn once tried to limit your network, which I still think was the right way to run it.
A popular marketing technique is to be the "Anti" company. I hope you can pull off the Anti-LinkedIn. The copywriting for that should write itself.
One more aside on recruiting. LinkedIn's infamous for terrible recruiters trying to fill quotas it seems. I don't know if recruiters need limits on messaging people or some type of ranking system.