Used tank water isn't important. When we do big water changes we introduce new tap water in our tanks, and it works fine. The substrate in the new tank should go on top of a layer of mulm from existing tanks. That jump starts the bacteria in the substrate. Given that you are combining 3 tanks, you could put uncleaned substrate from one of the tanks as the lower layer in the new tank. That really does jump start it.
The plants and rocks will be covered with bacteria, so that gives you the primary start for the water in the new tank. Adding to that, the pre-cycled filter or filters, and I don't see you having any cycle occurring at all in the new tank.
I switched from a 29 gallon to a 45 gallon tank a couple of years ago, doing much as you are, and had no fish problems at all, so I know this works well.