Adjust width of dialog box overlay

I have some specific layout requirements for a site I'm building, in that the pages are being displayed within an iframe in another site. I'm running into a problem with the dialog box that appears in an overlay when adding media on the node edit via a media field. The width of the overlay is being set dynamically, and it's always too big for the space. In the iframe, the essential parts of the dialog box are inaccessible to the user (screenshot attached).

I hate hacking, but I really need to set this dialog box to a fixed width on this particular site. I can't figure out where to do that in the module. Can someone point me in the right direction, or offer any other solutions to this issue?