Aftermarket EGT gauge. My EGT probe is installed preturbo. When it falls below 300 degrees I shutdown. There is some debate on installing the probe pre or post turbo. Part of the reason for the cooldown period is to make sure the engine oil that flows through the turbo does not keep cooking and leave deposits inside the turbo. The five minutes wait time you mentioned would also achieve 300 degrees or lower.
If you purchase an automatic transmission it's a good idea to monitor this too. Stock or modified.
Genosgarage.com is one of a few decent online places to purchase Dodge items.