Rinse the watermelon well and dry it with a towel. Roll it on the counter and look for the flattest side. A steady melon makes every other step easier and safer.
Cut about one inch off the top of the watermelon. Set the lid aside so you can use it later as a cover. Go slowly so you do not crack the rind.
Use a large spoon or ice cream scoop to remove the red fruit. Work in circles and leave a thin layer of flesh on the rind. Drop everything into a big bowl and remove as many seeds as you can.
Turn the melon on its side and look at how it rocks. Slice a thin sliver off the bottom so it sits level. Do not cut too deep, or you may open a hole you do not want.
Use an apple corer to push a small hole near the bottom of one side. Keep it about two inches above the table so cups fit under the tap. Twist the corer gently instead of forcing it.
Use a knife to widen the hole until it is slightly smaller than the watermelon tap. This snug fit helps stop leaks. Push the spigot in with a twist, and make sure it feels tight.
Blend the scooped watermelon in batches until smooth. Pour it through a fine mesh strainer into a large pitcher. You should end up with about six cups of bright pink juice.
Stir the watermelon juice with the grape juice, lime juice, and optional rum or vodka. Taste it and add a little more lime if it feels too sweet. Chill the mixture if you have time.
Place the melon on a tray or large rimmed plate. Add the ice, then pour in the punch until it is about two inches below the rim. Top with the soda and stir gently so you keep the fizz.
Drop in blackberries and lime wheels so they float on top. Hang a few gummy worms over the edge of the melon. Set the lid back on, place cups nearby, and let guests tap their own drinks.