To tin the part, you pre coat it with solder. Applying solder and flux to a clean joint and hoping that it bonds when heated is a crap shoot.
To tin the parts, put some solder paste on the part. Make marble size piece of steel wool. Drag it through the flux. Heat the part just enough to melt a piece of solder you placed on it. Use the steel wool to rub the solder on the part. Grab the steel wool with needle nose pliers to avoid burning your fingers. Once you have some solder on the steel wool you can heat the part and rub the solder on it. It is simple to evenly coat the part with solder this way. If you have a resistant spot the steel wool will clean, flux and tin the area while you rub.
Once cooled and cleaned of acid flux, add rosin flux. Rosin flux can be bought from electronic supply places in liquid form. Rosin is not corrosive, acid flux is. OK, Then wire, wedge, clamp the rib to the barrel. By heating both parts you will get a perfect joint. Heat the larger part, in this case the barrel. the heart will transfer to that rib. Work you way down the barrel and add rosin core solder. There is no need to heat it all at once. The rosin core solder wire added will be sucked into the joint and fill it 100%.
It does not matter what kind of soft solder you use.