I agree with Takeshi, couple additions.
If you do go the route of changing your search URL structure etc. I would not deindex your old search pages, I would 301 redirect them to the new pages you are creating. I would then setup new search pages behind a folder that you disallow in robots.txt to keep Google out of those results and into your more important pages.
The apples to apples comparisons make sense too. Product pages always convert better as it is the page where the product "lives"
I can see why Google ranks your search result page for "RevoStock Fishing Boat" as it gives users the best options for accessing all your fishing boat videos.
http://www.revostock.com/SearchResult-Empty.html?text=fishing boat&cat1[]=1
If you look at any of your fishing boat video pages on that search result page, they are pretty much identical examples I see at least 40-50 product pages like this
http://www.revostock.com/Stock-Video-Footage/229719/Fishing-boat.htm
http://www.revostock.com/Stock-Video-Footage/229730/Fishing-boat.htm
http://www.revostock.com/Stock-Video-Footage/229746/Fishing-boat.htm
same URL, title tags, h1, even the slug at the end Fishing-boat.htm etc just the variation with the ID in the middle of the URL and on the page.
Google is looking for the authority page on your site for "Fishing boats", but with all the product pages almost the same, I can see why it would point to the search result page as it is a major hub for your content You also mention that "On the product pages, we do show the keywords related to the item and then link back out to the Search Results pages from these. " This is another signal to Google that those search result pages are important.
Getting back to the conversion point again, you still should look towards using a category page to rank on your head terms vs the product pages due to your inventory. Lets say you wanted to rank for "Fishing Boat Footage". What product page would you send someone to? You have a ton of choices on your site and so seems to make sense to have a great category page to get people to the site on a given KW and then make it easy to then let them browse your inventory.
You can then use all the videos/product pages themselves to focus on the long tail searches. You need to work on differentiating the videos. They need descriptions and more information around them. I can see the differences in the videos by looking at them, but Google will not due to the lack of text. Outsource some writers to work all of this up and it should not only be good for Google, but for users. All of the detailed descriptions around the videos would help for those longer tail searches and you could end up with more search volume long term. I help run a site where we have "contributor submitted content" as a part of information about their products. The stuff we got submitted sucked. Poorly written, typos, not helpful, etc.
We hired some contract writers on the cheap and they cranked through stuff and the site is doing much better for having clean up to date content. I know you are saying, "That is crazy" but it is just the thing that will also differentiate your content from others and ultimately gain more customers (IMHO).
My best advice is to read everything that Adam Audette has ever written. I kid you not. He gets into details around pagination and structure for exactly the type of questions you have.
This article should nail it right on the head for you
http://www.rimmkaufman.com/blog/site-search-dynamic-content-and-seo/01032013/
An oldie but a a goodie
http://searchenginewatch.com/article/2097061/SEO-Techniques-for-Large-Sites-How-to-Maximize-Product-Visibility-in-Organic-Search
Cheers!