I have also read that you can cycle your new tanks "fishless" buy going to the grocery store and buying one raw shrimp. Unshell it and throw it into your tank after you set it up and monitor the level for several weeks. It can take WEEKS to cycle a tank. This is why a lot of people do not cycle their tanks with fish in them. It can end up being weeks of stress on the fish. No one can say it will be three weeks or two weeks, you have to know what you are looking for in your parameters to know your tank has been cycled.
Ammonia at 1ppm isn't that bad, though it isn't that great. It could be worse, but honestly the more water changes you do the longer it will take your tank to cycle. You can buy products to neutralize the toxins so they won't kill the fish in your already stocked tank. The down side to this is that you will most likely get false ammonia readings after that point so you have to keep a look out for the nirtates. Once you see the nitrates. The false readings will go away with water changes and such. I would do weekly water changes of 20%, but remember the more you take out the longer it is going to take to cycle, so don't freak out and pull 70% out trying to fix your ammonia levels. But I would let it go as long as you can (without over stressing your fish).
I would NOT put any fish in your new tanks until they are fully cycled. (meaning you start getting your nitrate readings, and your ammonia is down to zero.) Like I said you can cycle your tank fishless, since your other tank is not cycled yet you can't borrow the filter media as suggested above. That would be perfect if your stocked tank was actually cycled, unfortunately this appears to not be the case as mentioned before since you are not getting any nitrate readings.
I would set up your new tanks and give them at least a month. I have had success with the "Cycle" product. The only problem with buying products like these is that they are LIVE bacterias, and sometimes shipping kills them. Check the date on the bottle is you want to buy it, and if you want to try it, get it from PetSmart and if your nitrite and nitrate level don't change AT ALL within 24-36 hours, take it back and tell them it didn't work and get your money back.
I hope i helped some,
Kitten