Place the onion chunks in the food processor and blitz them until they are super finely chopped. Scrape into the center of a clean tea or flour sack towel, twist and squeeze it over the sink to remove any extra moisture. Use your hands to combine them with the remaining gyro meat ingredients. Cover with plastic wrap and let the mixture rest for at least 1 hour but up to overnight in the refrigerator.
Preheat the oven to 325°F and bring a pot of water to a boil.
Working in batches, pulse the meat mixture for a minute, or until it is a tacky, thick paste. Press it a little at a time into the loaf pans, taking care to eliminate any air pockets. You should have enough meat to fill 2 standard bread loaf pans. Press down firmly on the surface of the meat to even it out. Place a wet kitchen towel on the bottom of a large roasting pan and position the loaf pans on top of it. Pour the boiling water into the roasting pan. It should be 2/3 of the way up the outsides of the loaf pans. Carefully transfer the roasting pan into the oven and bake for 50-70 minutes, or until the meat measures 165°F on an instant read thermometer inserted into the center of the loaf.
Carefully remove the loaf pans from the roasting pan and pour off any fat that accumulated. Put the loaf pan on a heat-proof surface (a cooling rack or a pan on top of the oven) and place a foil wrapped brick directly on the surface of the meat. Let the meat rest like this for 20 minutes. After 20 minutes, remove the brick, run a knife around the edge of the loaves, then gently turn the loaves out. Wrap them tightly with plastic wrap and chill for several hours or overnight to allow them to chill and firm for easier slicing.