Possible issues :
1. Dead fish which you havn't found.
2. Nitrosomonas (the bacteria which convert ammonia to nitrite) function and reproduce less efficiently below Ph 6.8 - yours being 6.5 - and proportionately less efficiently the further you go below that (source : Hovanec
http://dataguru.org/misc/aquarium/waterinfo.html#NitrifyingBacteria).
3. They are autotrophic - get carbon from CO2.
4. They function/reproduce less efficiently at low temp (probably not in an issue in your case).
5. They also require oxygen to grow.
You could try adding CO2, adding an airstone/bubblewand, raising your Kh by adding sodium bicarbonate, which would also increase Kh.
However, I think it is still very strange that you have apparently no growth of nitrosomonas,
and your regular large water changes are also having no impact on the rising ammonia. This makes me think that either your test kit is faulty, or there is ammonia in your tap water (so test your tap water too).
What test kit are you using ? I gave myself a quick heart attack with a new test kit (had been using API, using it again now) which told me I had ammonia at 3 ppm until I realised I had transposed the result versus Ph on a graph chart that comes with the test kit wrongly.