The surest and easiest method to accomplish your tank transition kimbucktu, is with a sponge filter. I can't tell you how many tanks I've started this way and have never had a cycle prob.
Sponges have so much surface area that they are the ideal for bio filtration. Using an air pump forces water through the sponge and accelerates the process. Simply run one in your existing tank for a week to 10 days. Move the filter and fish into your new tank at the same time. Allow the sponge filter to run in your new tank until the good bacteria has had a chance to establish itself in your new filter. Then remove it if you don't like the look.