Coke contains a weak phosphoric acid as does most sodas. Tannic acid I have never used but will look at it. I use EvapoRust for all my derusting projects. I restore old woodworking planes and tools. EvapoRust is a nonacid, pH neutral, eco-freindly solution that removes only iron oxide and does not touch anything else. I have even soaked wood handled tools in it and it did not bother the wood or the paint.
I use it on all my tool tops to remove and prevent rust. It works great on cast iron since it goes right down in the pores and cleans them out. Some always stays there and prevents further rust. I also use it to remove rust and corrosion from the steel parts of antique model airplane engines.
I have used it to remove rust from an assembly that defied disassembly. The screws were rusted in their holes. I submerged the thing in EvapoRust and in 24 hours I was able to remove the screws and take it apart.
It can be found in many auto parts stores. I get mine from theruststore.com which shows several examples of how it works. The military uses it to remove the rust from tank chassis that are being refurbished.
I am in no way connected with Evaporust. I just think it is a great product.