Let's see if we can get some of the mystery out of this and look for a course of action or multiple courses.
The Mystery of the Rising Nitrates.
Let's keep it simple for illustration purposes. Our measure for NO3 is one (1) unit. Your tap water contains 20 units. Your aquarium naturally produces (20) units in a week. With me?
Week One
20 units from the tap
20 units from nitrogen cycle
40 units total
50% water change leaves 20 units
add back in 20 units from the tap (refill the 50%)
Week Two
Starts with 40 units
Tank generates 20 units from the nitrogen cycle
60 units total
50% water change leaves 30 units
add back in 20 units from the tap
Week Three
Starts with 50 units
You can see the trend. You cannot stop it without changing out 100% of the water every week and that would still leave you higher than you want to be based on your tap water.
I think you need a multi front attack.
Scavenger resins will only reduce a small portion of the NO3
Large water changes using another water source with much smaller amounts of NO3 will clearly help.
Plants will eat up nitrates.
Filter changes weekly.
Through and deep vacuuming of the gravel weekly.
There is equipment out there that will extract NO3 but is very expensive.
Hope this helps,
Regards,
Jay