Simple city. Mechanically rub the brass with scotch brite or gently with steel wool. Strip back the wire to bright copper and dress/pretty the end. Generously pre-tin both pieces with rosin filled solder and your 125 watt weller soldering gun... then gently (lower heat) finish soldering while holding together with steady hand. Heat just until the pieces marry well. If you screw up by overheating, just wipe liquid with a paper napkin and do it again.
Tip for pre-tinning is to use a low heat to keep the solder thicker. Higher heat is good for making it spread to where you want it to go. Solder will flow to the heat if the surface is clean.
Your brass is pretty thin. I'd make sure it is shiny clean (important), gently put it in a vice , held at the edges opposite the joint, and heat the (thick) wire first and add some fresh activated rosin "Kester 44" flux core eutectic Sn63/Pb37 solder (maybe 0.04" diameter) , remove any excess, bring the two into contact with a temperature-controlled soldering iron and feed the rosin-core solder into the junction between the brass and the wire and the soldering iron tip (holding the solder with your third hand, of course). Should only take seconds per joint. You can clean up in solvent such as lacquer thinner, but it will leave some insulating residue so you may be better off not cleaning the brass.
If 'twas me, I'd use a much thinner wire, maybe AWG 22.
NOTE: DO *NOT*, I REPEAT, *NOT* USE ACID FLUX OR ACID-CORE SOLDER as sold for plumbing applications.
You either use clamps, or your mouth at that point, unless you can actually get help that's actually helpful. But it's also another pint where having a reliable mechanical connection would men less having to hold the work together.