cycle and water problems

I've set up a new 60L (15 gallon) tank, with a few fish and plants,
and have been waiting about a month for it to cycle.
I'm using a whisper 20-30 gallon filter with carbon and a bio 
sponge. I also borrowed a handful or two of gravel from the
(excellent) local fish store to start things off.

The ammonia did drop from initial high spikes, but it has been staying
way too high, between .25-1.5mg/l according to my tetra test kit. So
I've been doing small (5-10%) water changes daily (with a gravel
cleaner), and adding Cycle as recommended.

Today I finally realised something was off and tested my tapwater.
It's pH 9, and has at *least* 1.5 mg/l ammonia.  Testing after I
add dechloramine stuff makes it even worse, nearly 3 mg/l!  What
can I do?  I don't think my filter has specific nh4/nh3 removing
inserts.  I have access to reverse osmosis water, but I don't
want to try and condition it, as I'm in favour of natural systems
as much as possible.  Would adding more plants help? Can
ammocarb be added to the tank water?

The fish actually seem fine, I don't see any gasping and they swim
around randomly, but it can't be good for their long term health.  The
snail does seem to be decimating my plants.

thanks in advance
Ivy