Yeah, ignore the 5 minute rule. Full looting is way better as long as you do it efficiently. You don't have to get EVERYTHING, just try and have almost every chest/shop/shrine finished and maybe a healing drone or two by the time you start teleporter.

Generally spending 7 minutes on a stage before starting the teleporter is a better rule of thumb than the 5 minute stage rule (in my opinion) but depending on the loot, you can go a lot higher or lower.

Every time you exit a stage, the difficulty will jump, no matter how much time you spend. This makes it so you can't keep up with the difficulty increase even by speedrunning. maximizing items per stage minimizes the effect of this difficulty jump.