Making large batches of syrups and sauces without reducing the majority of what I originally started with?

Follow the recipe and increase everything by the same proportion if you want to make more instead of just adding more water. You've octupled the water but kept everything else about the same. Of course you'll have to boil off all that extra water before the consistency is correct. If you had a recipe for a gallon of lemonade but wanted two gallons, would you add an extra gallon of water to the original recipe and expect it to taste the same? Or would you add more lemon and sugar in addition to the extra water to keep the flavor the same? Same thing here, adding more water will water it down, you need to increase everything to increase the yield and keep the consistency the same as the original.

Interestingly that page even has a button to scale up the recipe. Click it and you'll see it does exactly what I say here: it doubles or triples all ingredients.

The problem is not that you need more water, but you need less to start. There's water in the teriyaki sauce, water in the soy, and water in the whiskey, and you're adding 8 more cups too that. When you cook the sauce down you are evaporating water out of it until you have the consistency and intensity of flavor you want, you could start with half the water in that recipe and get to the same place a lot sooner. You may find 2 cups of water rather than eight is just fine, you'll work that out by making a batch or two.

I don't know why the recipe you found has so much water. It's possible the person who put it together liked it runny rather than sticky, or perhaps they just didn't have the balance right, but the answer you are looking for is adding less water. You'll still want to cook it down as you want the flavors to develop, just not as long. You'll still end up with 2 cups though, so if you want more you just need to multiply the ingredients to the figure you want.