I love this question!
This is a creative solution for you to try out ;)

1. If you have the capabilities create your own SEO page/landing pages with just the right keywords. Have these landing pages 301 redirect to your own original website (assuming you have one).
2. Embed both a video (per landing/SEO page) and picture of eithe related context or screen shot of video.
3. Leverage Pinterest: their platform is a collection of hand picked topics and that is just what Google uses to rank its findings, if your landing page have good SEO and you pin the pin the images to Pinterest with good descriptions (as it would be searched for) your videos could be thus promoted as Pinterest shows high in google searches.
4. Have these landing pages focused as conversion: goal? Watch one or part of the video and go to YouTube for more or the rest. That way of your goal is monetization you capture views on YouTube and not just landing pages.
5. Have content description exactly as someone would search in your website about the video in mind and link it to YouTube.

This SEO tactic will increase both your websites traffic, but also YouTube views. :)

Tweak or create variations (a/b testing) of the landing pages to find the optimal design/wording/video for each targeted audience per landing/conversion page.

Best of luck! If you like my advice please follow me here on Clarity. https://clarity.fm/humbertovalle