I've seeded 6 tanks (7 if you include the fact we moved the first tank 1000 miles and I had to seed it again when we got here) and seen only fully cycled results on tests.
I run more filtration than required. I also run filters which share a type of media insert, etc.
Here's a step by step of what I do...
Setup the new tank with it's gravel, etc, let the filters run, make sure there's no issues with the equipment. Then turn off the filter, heater, empty the water.
Take 50% of the water from old tank and put in new tank.
Refill old tank (basically you just did a 50% water change on your old tank).
Top up the new tank, turn on your filter (you have just 50% water changed your new tank). Turn on heater. Make sure old and new tanks read as same temp. Because you have the same source of both old tank water and new tank water, pH etc should be exactly the same in both tanks.
Put some of your filter media from your old tank into your new tank. Don't replace all as you have to leave some in your old tank. This is one of the reasons I used to run multiple filters on each tank.
Put some of your gravel and/or ornaments from the old tank into the new tank. I would always move quite a lot of it and leave it in the new tank, but if your new tank is very different, you can simply keep the substrate/gravel in a cup of piece of fabric which water can flow through and sit it in the tank.
Transfer a fish or two from old tank to new tank (should be no acclimation required if you matched temp, as I said if your old tank and new tank water are from the same place they should match). If they're staying there, great, if not, try to find a fish to put in there which has a bioload appropriate for the size of the NEW tank and what you intend to put in it.
You need to add fish SLOWLY. If you have a schooling fish to put in there, put small amounts in. Monitor the parameters closely and the first time you do a water change (if your water parameters are OK) do a smaller water change than normal. If your params are bad, then you need to do more water changes.
Anyway, that's me. Has worked every time for me. Obviously you return your starter fish to the original tank, etc, whenever you have your new fish for the new tank available.