How to get stable and long lasting high temperatures in charcoal grill?
I'm not sure how many steaks you're doing at once, but if you're not using the entire grill surface, stack the charcoal up. (Not sure how well it'd work with the entire grill surface and, e.g., two starters full of charcoal. With the grill open, it'll surely work.)

You can cook steaks with the lid off, that'll likely lead to the coals burning faster (hotter).

Stacking the charcoal does two things:


the stack is higher, so it gets the charcoal closer to the meat. You can't lower the grate on a Weber kettle, unfortunately.
there are more briquettes under the meat, each putting out heat.


A good stack is hot enough to brown a steak, even if you put it on the grill dripping with marinade (not that you should). Make sure to have a pair of tongs, you won't want your hands anywhere near it.