So the FAQ claims this is possible, but isn't clear what access level provides this or how to obtain. Is this restricted to mods/admins only? Do I just have to say 'pretty please'?

I don't seem to have this option anyplace, but the place I'm focusing on right now is creating a poll in 'General'.
How do I create a poll?
When posting a new topic or editing the first post of a topic, click the “Poll creation” tab below the main posting form; if you cannot see this, you do not have appropriate permissions to create polls. Enter a title and at least two options in the appropriate fields, making sure each option is on a separate line in the textarea. You can also set the number of options users may select during voting under “Options per user”, a time limit in days for the poll (0 for infinite duration) and lastly the option to allow users to amend their votes.