Here's my take on the scenerio from the limited information given...
...You started your "new" 20 in the new house...and your two and a half weeks into a new cycle??
Hopefully you kick started/fed the cycyle with a dead shrimp or something?? I'm probably reading a lot into this but...You saw an ammonia spike then 0 and then a nitrIte rise?? Then you added this "cured" LR and the ammonia is going up again??
If any/all of this is true then I'd say your probably on track for the next two weeks...
Whatever cycle started over the last two weeks was probably coming into balance with it's current bioload...adding the "cured' LR added to the load and additional bacteria need to grow to balance this level..
As long as the LR was basicly cured and is only adding a small amount of organic waste (even good LR will have some dieoff from transport) the secondary growth spurt of bacteria will be quicker then when you started with a fresh tank...
This is because the nitrosomas (ammonia to nitrIte) and the nitrobacter (nitrIte to nitrAte) bacteria multiply expotentialy ie:1-2-4-16 and already being present and starting with a fair number from the first "mini" cycle will now multiply at a quicker rate to "catch up" with the new bioload.
The other suggestions of prepared water for small WC during finish of cycle and possiable addition of a bacteria "seed" will also be helpfull...as you may still be in the finishing stages of a cycle two weeks from now when you add the fish.
Don't forget that the nitrifing bacteria are also oxygen consumers so you want to make sure your tank has aeration/circulation and possiably an airstone for the next week or so to "help" the bacteria grow...
And keep testing your water parameters because as you probably know a smaller tank is more tempramental/less forgiving than a larger tank as far as PH and SG as well as the nitrogen processing goes.
Good Luck,
(and let me know if I'm even close)