First off, I would not recommend doing this to any fish like a ciclid because of their needs. But if you absolutely have to do it, this is the best I can recommend.
If you absolutely have to put them in the new tank, put as much gravel as you can from the old tank, split the filter media with the new tank, add any and all decorations that you possible can, get some more gravel from the LFS and if you can some more used media and then pray for the best.
The cycle might be cut in half but it will not complete itself for a while. You still need to be very diligent with testing for ammonia and nitrites so that your fish don't suffer and try to have lots of suitable water conditioned and equalized with the tank water just in case you need to do a lot of water changes.
The only other way I can think of that might help to cycle faster or at least protect your new fish would be to link the two tanks together with pvc pipe and powerheads so that the established tank can handle some of the ammonia and nitrites while the new one gets it's own biological process going. I would still get as much seeded material in the new tank as possible but that is the best way I can think of to set up an "right now" tank. Just make sure the tank tops are even with each other.
I have not used it and I have both good and bad things about BioSpira but if it has a chance to wrok and won't negatively effect the tank, I would try it. Just make sure the LFS has it stored properly and it is a fresh batch.
Last, even though I have heard ciclids will eat plants, get a lot of them! Fast growers and very bushy plants like elodea, java fern, java moss, hornwort, other mosses or whatever else you can get ahold of to try and help with the ammonia. They will NOT help the cycle but will help to protect the fish from the ammonia assuming it doesn't reach toxic levels.
Just don't get complacent if the cycle "appears" to have finished. I can only imagine the possible effects of a fast start if things get really out of balance and your tank crashes. Don't mean to make it sound like a horror story but better to make sure you have all the bases covered instead of having such a great deal become a great disaster.
Ammonia will also help, never thought of using it in a fast start but you need a food source, nice catch musho. I would have used food but it wouldn't be as effective in a fast start. Just test, test, test and retest! ;)