Lars and crdlb, thank you so very much for your suggestions. crdlb, I wasn't able to drag and drop into the program (it has a tree structure with checkboxes next to each folder), but, as it turns out, following Lars' reply actually led me to find another solution. I realized that I was able to connect to the server with the regular sftp client, so I knew that my connection settings were correct. I then went back and re-read all of the manual pages for sshfs and found that I had misunderstood how to set up an sshfs connection before. I needed to add a specific directory on the server that I wanted to mount to my local computer:
I hadn't been including the server-folder-name. Mea culpa.
sshfs [username]@ftp.servername.com:server-folder-name ~/local-folder-name
I'm writing all of this down here in case anyone in the future has a similar problem. sshfs definitely seems like the best option for me to mount a server folder to a local folder, then, and is almost just as easy as using Nautilus' "Connect to Server" option. Again, thank you both!