Shower faucets exist that will keep the temperature the same despite pressure differences in the plumbing system -- like when someone flushes a toilet. To see details about this "pressure balancing valve", go to "Nuts & Bolts", enter the keyword "shower" and look for "How to stop shower scalding". There you will find a full animation that explains how this valve works.
I do have to make one correction to the TV segment. When I talked about how easy it is to reverse the hot and cold sides of the plumbing, I showed turning the brass shaft over. In fact that was something that was quite unclear in the valve instruction sheet, and after finding that it didn't work well the next day, I discovered that you pull the cylinder out of the valve and reverse the white tabs -- then it works. Yes I talked to Moen about changing their instruction sheet. That's one of the
perks of my job -- they might listen to me.
Soldering pipes in a tight space really requires some flame protection. In the old days we had really efficient asbestos sheets -- but of course we don't have the asbestos any more. So today you can buy cotton face cloths that have been impregnated with fire retardant materials. When exposed to flames they turn to charcoal and disintegrate, but they don't burn. Just buy several before you get started on the job.