My take...
Robb,
You have the tuner that is going to do the heavy lifting. Depending on power levels it will match 6-3200 ohms which is a wide swing for a tuner compared to a transceiver that has a built-in tuner. One reason an external turner has an advantage over internal.
For 1/3 the cost you can buy a DX Engineering dipole/doublet antenna. It will have all the hardware and the 300 ohm feed-line for the balanced input to the tuner. 70 foot for 40m and up and 135 foot for 80m and up if you have the room. You can tune a lower band for that length, but the loses will be higher and the antenna efficiency will be lower.
I don't have a fan-dipole, but all the reading suggest a tuned antenna setup and no tuner. That's the reason I believe the information for the two together will be limited.
My setup is an SG-237 coupler and DX Engineering 70 foot antenna extended by 15 feet on each end. The feed-line to coupler is somewhat unconventional. One side of the feed-line to the ground stud on the tuner and the other side to the ceramic stud on the tuner. Tuner is under the eves of the roofline and the 9 foot coax from the tuner enters the house via a window.
You have a balanced line output so you are in better position than my setup. I don't believe a fan-dipole will improve your setup. So hang some wire and see what happens. Theory is great and it keeps from making poor choice, but in the end most setup are a compromise from the optimum configuration.
I made a contact with CE4CT yesterday evening (gray-line) with the above setup using a IC-7000 set to about 85-90 watts PEP on 15m. Likely he has a huge beam pointed North, but the contact was made. 
According to QRZ he is 5000 miles out on the tip of South America.
