I need a thin, bendable sheet metal that I can solder copper wire to. Thanks!
Well between going up and down hills and leaning into turns it is rarely level anyway. As long as its not so far out of level that you're getting air into the lines you should be fine. I would say try bleeding the brakes. Its possible you turned the reservoir upside down when changing the handle bars and that would have let air into the lines.
If the fluid line exits at the top of the the reservoir there may be air in the line. I have no idea of how to bleed and refill it on an angle because fluid will over flow the bottom of the reservoir without filling the line.
Tin - available in the KS Engineering flat metal displays that also have copper and brass. While plain steel can be soldered, stainless steel in the assortment is a bear.
copper. you could also solder copper wire to bronze or brass. Copper sheets come in different gauges like wire. Read up on annealing copper, that will make your life shaping copper much easier. You will need a cheap plumbers torch for it. You can obviously also solder copper to steel, but the steel will less easy for shape. It will be cheaper though.