Drain the tofu and pat it dry with a paper towel, then place it on a large plate lined with several layers of paper towel. Put several more layers of paper towel on top, then place a cutting board on top of that. Weight the cutting board down with something like several cans of food or a book and let the tofu press for at least 30 minutes (preferably several hours).
While the tofu is being pressed, prepare the marinade for the tofu. Mix the vegetable broth, tamari, maple syrup, liquid smoke, tomato paste, mirin, fresh ginger, and garlic in a small saucepan and bring to a simmer over medium heat. Remove from the heat, let it cool slightly, then strain through a fine mesh sieve and discard the solids.
Once the tofu has been pressed, cut it into 4 slabs. Place the musubi mold on top of one of the slabs and use a paring knife to trim the tofu around the outside of the mold. Repeat with the remaining 3 slabs. Put the slabs of tofu in a sealable container and pour the marinade over them to coat them, then seal the container. Let the tofu marinate, in the refrigerator, for several hours.
Preheat the oven to 400 degrees Fahrenheit. Carefully remove the slabs of tofu from the marinade and gently shake off any excess marinade. Lay the tofu on a baking sheet lined with parchment paper. Bake the tofu in the preheated oven for 15 minutes, then gently turn the pieces over, brush the tops with more marinade, and bake for another 8 minutes. Remove from the oven and let cool.
Cut the nori into four 2 1/4-inch wide strips (you will have leftover nori).
To assemble the musubi: Put one of the nori strips, a long edge nearest you, on top of a sheet of plastic wrap, with the rough side facing up. Place one of the pieces of baked tofu crosswise in the center of the nori.
Place the mold on top of the tofu, matching up the edges.
Put 2/3 cup of the hot steamed rice in a small bowl and toss with 1/8 teaspoon of the fine grain sea salt. Put the seasoned rice evenly inside of the rice. Place the tamper inside of the mold, on top of the rice, and gently press it down to pack the rice. Keep the tamper in place and lightly press down as you pull the mold up and off the musubi, then remove the tamper.
Wrap the nori around the top of the rice, then wrap the plastic wrap around the musubi and set it aside to cool and set. Repeat the process with the remaining nori, tofu, and rice.