When the banding is shaped, use the third hand tool to hold the banding together at the cut edges and apply flux very thinly. I used a needle tip on my soldering iron and heated the banding from the inside of the circle while applying the solder on top of the banding. Solder runs toward heat, so all I did was swipe the solder along the joint and it applied really thin.

Important: You really need to use flux - all other attempts at soldering brass together didn't hold.

I used this one - bought it at the hardware store and it does the job:

I chose the thinner solder that came with the iron

My third hands set up - although it would make it third and fourth hands.... it gets hot - no way you can hold the part, the iron and the solder....

You can see how I used the iron from underneath the gap - and you can see how the brass changes color from the heat