I managed to figure out what I needed!
Indeed, the answer that worked for me is to pass along the cookie information that contains the login information for the site. Once I pinpointed which cookie was needed (I personally found this information with my Chrome browser in Advanced Settings, under “Privacy and Security” -> "Content Settings” -> “Cookies”), I used Mathematica's SetCookie function. Prior to executing the Import line, I ran something like this:
SetCookies[<|"Domain" -> "[INSERT_VALUE]", "Path" -> "[INSERT_VALUE]", "Name" -> "[INSERT_VALUE]", "Content" -> "[INSERT_VALUE]"|>];
I replaced all “[INSERT_VALUE]" with the appropriate information about the cookie.
I then executed my
line, and voila! I have the information I needed!