Hmmm...what else is in the tank aside from the RES? I agree with you, it's rather atypical to have such a slow ammonia rise without development of nitrites. On the other hand, really slow cycles are possible.
Another possibility off the top of my head: something is happening to the bacteria to cause a die off, possibly during water changes.
You might try upgrading the filter-- it would be really hard to overfilter a tank with such messy creatures in it.
Here's a quote from
this webpage:
My rule of thumb is arrange filtration rated for a tank 3 times the size of what the turtles are in . Do NOT factor in only having the tank partially filled; a half-filled 20 gallon tank should get a filter rated for a 60 gallon tank, not a 30 gallon. This assumes a ‘turtle load’ of about 3 turtles up to a year old in a 20 gallon long, perhaps 4 adult basking turtles in a 75 gallon tank, etc…
EDIT: I just reread your original post and had another thought:
It's not so much how many times the water turns over in the tank, but primarly how much capacity your filter has to house bacteria, and then how effectively your filter can expose the resulting bacteria to well-oxygenated water containing nitrogen.
If your filter is rated for a 20g tank, you will probably have inadequate bacterial colonies to completely convert ammonia to nitrIte. You *will* have a sufficient amount of bacteria to convert *some* ammonia to nitrIte. You will then have a vanishingly small amount of nitrospira to convert the nitrIte to nitrAte.
This would explain the slow rise of ammonia, the zero nitrItes, and the low nitrAte reading.
My conclusion would still be to get a larger filter as the quote above suggests.