Hi Tyler,
"How on earth do I make 1,000 pages for similar topics?" Do you have 1,000 keywords?
I would not recommend building 1000 pages to your site just to have massive amounts of content. However, as you described "the opportunity to more specifically answer a users query." is the goal.
Instead of focusing on building 1000 pages focus on what your users are looking for and the best time/way to deliver that message. Weather its social media, guest blogging, attending an event and doing a massive PR, experimenting and optimizing will drive results.
Ideally you want to create a page targeting 1, 2 keywords max, and build links to these pages via an internal blog (If you do not have a blog on your site, add one). A user will most likely scan a page in 5 seconds and if they dont find what they are looking for they will look for another result, so make sure the content you are creating is relevant to the searchers keyword phrase typed. You can discover how your users found your site in Google Analytics and tweak the page to serve the user efficiently.
Hope this helps