My method is very similar, but I find even just a tablespoon of yogurt from the previous batch is enough to inoculate 1 gallon.
We also drain off a good portion of the whey using a nut bag to make Greek yogurt. The leftover whey we put in smoothies.
I LOVE being able to control how much sugar is in it, and it’s way cheaper than buying individual packs. All in it costs us right around $2.50 for a gallon of yogurt at home.