I too am in a fish in cycle and was fighting to keep ammonia levels down (now fighting nitrite levels.) If my levels get to .25 ppm of either ammonia or nitrite I do a 70% water change. I have done 2 back to back to get it down as well. But the levels you are talking about are 16-30 times as high as what I have seen. While everyone is right in telling you that you need large water changes quickly I would do a full 100% water change instead. I did this when my ammonia reached .5 ppm one time. All you need is 2 clean buckets, fish net, and dechlorinator. By clean buckets I mean something that has never been used for harsh chemicals (like paint) or soap. Those chemicals can leach into the plastic of the bucket and then release back into the water when it is filled. Then take one bucket filled with tap water the same temperature as the tank and dechlorinate it. Net your fish from the tank and put them in the bucket. Then shut off your filter and make sure it stays wet while you drain your tank. Siphon all the water from your tank (I use my gravel vac and the other bucket dumping it when it gets full.) Then use the same method in reverse to fill the tank back math the water temp into the bucket, declorinate, then siphon back into the tank (that way you don't disturb your plants, gravel, decorations too badly like you would with a high pressure hose or just dumping a bucket in.) Once your tank is filled turn your filter back on and net the fish back into the tank. With small tanks like yours and mine your fish will only be out of the tank for a few minutes and this will be less stress than the bags you brought them home in. If you are really worried about the fish in a bucket you could drop an air stone or depending on your filter, run the filter in the bucket while you work on the tank.
This should drop your ammonia to 0 ppm assuming that you have no ammonia in your tap water. The fish will start producing ammonia as soon as you put them back in the tank so you filter bacteria wont stare from lack of ammonia and they won't be exposed to any chlorine from the tap if you declorinate in the bucket before you put it in the tank. Also be prepared to do 20-60% water changes daily until your cycle is complete.