cold water too hot in AZ—worth it to insulate attic copper?
This is the same theory behind insulating the hot water pipes in attics in cold climates (freezing concerns aside). It'll help but only for a little while. It might extend your hour-long window of continued cold water to 2 or 3 (or more) hours, but you won't keep cold water all day long.

If your attic is easily accessible, the pool noodle pipe insulation is cheap enough and easy enough to install for this to be a good trial. Not much lost if it doesn't work out. If that trial goes well, then you'll want to consider if more expensive solutions are worth the time and effort to install.