Stevangelista actually pointed me in the right direction, I wish I could mark comments as answers, and since I'm new I can't upvote the comment, but here's the solution:
I am using a customized master page, and that comment had me take a look at the elements in the page.
Since the master page is being used in the dialog boxes as well, I used the s4-notdlg class to remove parts that weren't needed in the dialogs. Those parts were pushing the buttons below the bottom of the screen.
I'm not a css expert, so there may be ways of keeping those parts and still have the buttons accessible, but the particular issue I was trying to fix was resolved by using the s4-notdlg class to objects in my custom master page.