Then we carved out each name with a dremel and a carving tip - here's James in action. This was the most time-consuming step - each word took 15 minutes on average to carve.
Here's an example of how they come out after carving. Nice!
Then we used a dark wood stain (color: Red Mahogany) to darken the areas we carved out , wiping excess of the polyurethaned area with a spare cloth. We didn't get to it, but the next step would be to put a final coat of polyurethane to weatherproof the whole sign, and drill holes in the bottom to insert a peg so each sign could be staked in the ground next to each tree.
Possibly related to my pickyness, it took us a while to decide on the actual method we would use to make each sign. Some of our trials/errors are displayed below, including painting inside the letters, using a wood burner tool, and carving outside rather than inside the letters.
Alas, we had to fly back to Boston before seeing the signs installed in the backyard, but I'm hoping my mom will send me pics of them all set up!

