I'm going to basically try to follow what the copper's doing, except there will be more runs down to the basement than there are now. That means I'll have to widen the existing holes a bit.
I will get one of those tubing cutters. For larger sections where there's a bit more room I'll probably use the reciprocating saw just to save time, but for close quarters, the manual cutter will be a lot cleaner and easier.
Regarding the stagnant water thing, isn't the solution to that to just let the water run a bit before drinking, and to use thinner tubing to those fixtures?