Only three days into the cycle: Ammonia down, NitrIte and NitrAtes present...

I would not use the sponge from your other tank if it is the only sponge. Just some gravel in a media bag would do it but I think as fast as you say this is going that the ornaments you put in at the first have things started. But that said, more gravel could only help. Put it somewhere where it will touch your gravel or biofilter media so the bacteria can transfer and spread easier.
 
The bacteria do not reproduce any faster at 4ppm than at 1ppm; if there's readable ammonia they're going full pelt. The reason for ensuring that there is 5ppm at the time you add the ammonia is to make sure that the bacteria don't run out before the next addition.
 
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