I would brine is because that would be easiest to get right. A teaspoon is a 1/3 of a tablespoon so you are missing 2/3 of your salt. If you brine it 2/3 of the brining time than you will put the missing 2/3 salt in the cheese.
Prepare fully saturated brine (24%-26.5% salt, until salt is left on the bottom and the water can't absorb it anymore). Use it when it's cool (65°F or so). For each 1 lb of cheese leave it for 2 hours (instead of 3). At full brine saturation the cheese should float halfway at the surface so the top of the cheese may be out of the brine. Turn the cheese upside-down halfway through the brining period so both sides get equal brining. Don't forget to add calcium to your brine otherwise calcium will run out of the cheese. Let it dry on a rack in a cool place (50°F-60°F) for 2-3 days, turning it once or twice a day. When the outside is dry to the touch you can cave, wax, or vacuum it. It is important to get that outside on the dry side so you assure that the cheese has developed a basic rind.
In my opinion, cheddar after the curd has been pressed, milled, salted and re-milled is just too dense and dry for effective dry-salting.
In any event, a tablespoon is a strange measurement. Always weigh the cheese and calculate the salt based on the cheese weight.