It is likely that LinkedIn campaigns to warm leads (aka remarketing) could be a good fit, but LinkedIn campaigns to cold leads is only a good fit for a few narrow industries.
If you have extra ad spend to work with...
It's possible the impression share loss due to rank includes losing out on impressions that the campaign is eligible for but are very broad so you would not want to show for them anyway.
Cart Abandonment Campaigns & Cart Abandonment Audiences:
A high level overview of how SEO works...
Sometimes the ROAS will plateau...
Sometimes when the budget is limited, having too many products in the shopping ads means the algorithm has trouble gathering conversion patterns in order to optimize because each conversion on each shopping ad/product is too spread out across the weeks/months, so the answer is to temporarily exclude products until the algorithm can get the hang of things. Then, with scale later on, those products' shopping ads can be re-included. Just because we exclude a product, doesn't mean it won't be purchased. It just means it might not work well as a shopping ad & the money could be better spent on other shopping ads to bring people to the site...but those people still might buy these products.
Start new campaigns with a manual bidding strategy until the algorithm has enough data to switch to automatic. Then, see how high you can push the algorithm to automatically raise its goal (i.e. target CPC of $X could be the goal). You must have conversion tracking set up correctly before running any campaigns or else you will be feeding the wrong data into the machine learning algorithms, which will obstruct its ability to get results. You can check this by going to the Conversions report and checking the “Include in Conversions?” column and making sure that only the appropriate conversion actions are included.