Nitrate reactors are just places where water is pumped in very, very slowly, starved of oxygen and use anaerobic bacteria to break down nitrate. DeNitrate or Purigen (or a combo of the two) would be your best bet.
Trust me, I have done everything from 50% changes every 4 days to 50% every week and this is bewildering to me. I finally got my nitrates in my sw tank to drop to a steady 15 ppm because I have filled my refugium 18"x30" area full of calurpa.
5 sets of test kits here, I shake the heck out of them #2 solution shaken for 30 seconds. I follow the directions well, I use 3 out of the 5 kits to make sure my reading are right. I am a fanatic about keeping records of my water quality on all 6 tanks.
Were did you get the drift wood from. Some from boggy areas can ba real problem if not cleaned propoerly. Sorry, I just feel your pain. I would consider running a Fluval FX5 with a good filter media in it.
I have almost the same setup as you just with more fish. I change 30% of the water every 15 days. I think you should add some gravel to allow more healthy bacterea to grow and change the filters every 2 months. It works for me. It does seem very wierd how you keep getting them spikes though.
I used to have gravel, then went to sand and then to polished river rock, but fish waste would build up around the rock so that is why I tried bare bottom. Nothing has worked.