IF you completely empty your tank of fish, in a short time your ammonia will read 0. Then you will assume your tank is cycled. This is not true. Just because the ammonia read 0 initially, does not mean there is enough bacteria to sustain a bioload, just that the bacteria present has used the available ammonia.
To test and see if the tank is really cycled add a source of ammonia wait an hour and then test. If the test reads zero then your tank is cycled.
During this interm time where you have no fish I would continue to feed your tank like there was fish in it. Let the bacteria build up in the rocks and sand. Then add fish.
Large scale facilities use pure unscented ammonia. The kind where the only added ingrediant is water. If this is not availbale fish food will work fine. If you use the pure unscented ammonia you will have to do a WC of around 90% before adding fish as the pure unscented ammonia reaks havoc on the PH.
IME cannister filters are good. They will build up concentration of bacteria as well so in this time when you are short on the liverock, the cannister is supplementing additional biological filtration.
Also IME it is very possible to run tanks with a 3x-5x turnover rate per hour. It is actually recommended with keeping some species. More is better yes, depending on what you are going to keep.
If I were you I'd invest my money in some base rock (dried liverock) since it is cheaper and will become live shortly, and then in a couple of nice powerheads. I like the maxijets personally, I also love the hydor attachments.
Do you have a sump?
I'm also guessing that since you went cheap on everything else that you did the same for your cleanup crew, if so I'd get those before the powerheads. Just some snails (turbos, astrea, naussarius vibex,IMO Margarites are temperate and don't last long) maybe a few shrimp (cleaner, peppermint, blood), and some hermit crabs ( scarlet reefs IMO because they won't become aggressive and kill each other or your snails).
I agree that it wasn't your nitrates. I have had tanks sit at 20, I have friends who have tanks consistently in the 80's, they are not as big of a deal as they're made out to be. Ammonia is more lethal in small amounts.
Good Luck with your tank.