So, to keep levels down (as far as I know) there are two good ways to deal with it, Water changes, and plants. One way to speed up the cycle is to add more surface area to that tank. (like pieces of driftwood, more hiding places, etc) the more surface area there is, the more places the beneficial bacteria has to attach to and such.
I would suggest adding media from an already cycled tank, but seeing as your previous tank was so new I'm not sure how much of a chance the bacteria had to establish a colony... but if you haven't already, moving gravel and ornaments and stuff over (as long as they weren't aloud to dry out) should help some...
I've also heard raising the temperature on the tank will help the bacteria grow faster, just make sure not to increase it too fast or too far out of any of your fish's comfort range.
I'm not entirely sure how safe it would be with fish in the tank, but you could always add a live bacteria... Some of them get expensive though. Some of the good one's I've heard of are Seachem's Stability, Smart Start, and Bio Spira to name a few. some people swear by this and say it would be safe to use with fish in the tank, but personally I'm a bit skeptical on that. You could always use it on a bucket or other tank that has plenty of gravel (perhaps attach your filter into the tank or bucket you use the bacteria in as well) Most of these say they are overnight cyclers, but often don't do it that quickly.
happy owner of a wild type GFP axolotl named Percival and too many guppies to count.