Hello and welcome, Mayday. I've never made that before, but if you're cooking a thin cut of beef like a flank or skirt steak then high (450 and up), direct heat is the way to go.
I would say a minute on one side, turn, a minute, turn back for a minute, then back again for a total of about 4-5 minutes tops.
This way you will get a good Caramelization and get what's called a "bumper to bumper" medium rare. Your not trying to get beautiful sear marks with this cook since your slicing it up
Buckie is right about that dome temp. It will be higher than your grate level, so in hindsight if you were running at 300ish on the dome, your fire was not near hot enough. Get that cheap oven thermo, Try it again with direct, high heat. Flip often and also when you pull it off and after it rest for a few minutes, make sure to slice across the grain. This will give you a more tender and pleasant bite.
Hope it helps!
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