How to get rid of the rich iron and blood taste in certain beef cuts?

If your beef has honest-to-goodness blood in it, complain to your butcher.

More likely, what you're seeing/tasting is myoglobin, which does have a bit of a metallic taste when it's not cooked. You can get rid of this in two main ways: osmosis and heat. So here's how to do that.

1. Dry brine it. Put the beef on a drying rack set on a paper-towel-lined baking sheet. Salt liberally on all sides and set uncovered on the bottom shelf of your fridge overnight. This will pull a lot of the myoglobin out, while also improving flavor, juiciness, and texture. Pat it dry with more paper towels before cooking/searing later.
2. Cooking with special equipment. If you want to serve it pink with no metallic taste, you'll want to cook slowly, and at a low heat. That's where immersion circulators (i.e. sous vide) and combi ovens shine. If you have access to these, try cooking your meat to 135F (medium rare, closer to medium) and then sear in a hot cast iron or carbon steel skillet (maybe with crushed up garlic, thyme, butter, etc.)
3. Cooking with common equipment. If you don't have access to these tools and the cut of meat is reasonably thick (2" or more), then you can set your oven to the lowest setting (other than plate warming) and just wait. Use a good thermometer to detect when your steak gets ~10F below your target temperature, then transfer it to a screaming hot skillet to sear.

Please include a way or two that is 'quick and dirty' when time is scarce, and also allow for still being able to serve it on the rare/medium-rare end of the spectrum.

You'll need to dry brine it, otherwise this is a "pick one" situation. However, if you're cooking skirt or flank steak, then you can still get good results by cooking very hot and very fast, though it will tend to dry the meat out a bit more.