I'm going to go against the grain a little here and surgest you do nothing to help the levels along this early on. It is a fishless cycle, so the readings do not need to be low. Above a point, nitrite becomes toxic to the filter bacteria you are trying to establish, but this level is extreamly high (above where our kits test for)
The higher the nitrite level once the NOB's set in, the more stable I find the colony is after the cycle completes, and thus the less chance you have of mini-cycles once the fish are in
There is a cut off point, but you aren't likley to have found it yet... Nitrate is present, so unless it comes from the tap water, the NOB's are already at work
(Nitrie Oxidising Bacteria is the acronym NOB here guys, just to avoid the regular confusion
)
If you find that things aren't moving along, do a large (as near to 100% as possible) waterchange, and that should re-spark things
You shouldn't need to do that untill you're near finished though. Only do this if levels stop moving as they were a few days before, or if you find the levels have remained stable for a few days. Yes, skipping waterchanges will slow things up a little, but the increased filter stability after the cycle is worth the extra couple of days wait IMO
All the best
Rabbut
EDIT to add after seeing your reply; if you are upgrading and closing down the old tank, why are you bothering to cycle? Just do a full waterchange now to clear the nitrite and move the old tank's filter media across to the new tank with the fish. Bingo, instantly cycled tank ready to go, for the number of fish you had in the old one
Give it a couple of weeks to monitor it and ensure no mini-cycles occur (very unlikely of you keep the filter wet all the time, but remotely possible) and you are ready to slowly increase fish numbers in the new tank (don't more than double numbers in a week and you will be fine) and hey-presto
