Take the peels from the lemons and muddle with the sugar for a minute or two until the sugar is moist. Add the juice from the lemons, add the soda water, and stir to dissolve. Add orgeat, and whisk hard "in order to whiten the composition". Add brandy, rum, and Maraschino. Strain into a punchbowl, and add Champagne, stirring in gently.
A couple of things. I'm assuming that "2 bottles of soda water" in the original recipe would be the same volume as "2 bottles of Champagne". With the volume of soda and Champagne being equal, this is about 180 ounces, which means 1 drink = 6 ounces.
"How to Mix Drinks or The Bon Vivant's Companion", Jerry Thomas pg 72