To answer your question about recirculation reactors for pellets, simply yes! The main stories you hear such as yours are from using single pass reactors.. Geek, even I experienced the exact same thing when I first began with my 2lf 150.. Then,I stepped up to recirculation about 4 to 5 years ago(it's hard to recall because it's been so long that I've run them to be honest)..
Once you get into the recirculation with a "good"reactor, I would say, with the exception of one case that I have read about, that I couldn't figure out, your good to go.. None of the cyano, none of the stripping, none of the "add half at this point, or tumble like this, because of this".. And most importantly, none(once again, as long as you buy good stuff) of the sticking, and especially, none of the fiddling..
I will just say that as far as my pellet reactor, I have cleaned it two to three times max over the years.. I don't fiddle with the valve(effluent), and I pretty much dump the pellets in(i put in, and have, since after my first fill and learning about the reactor, full doses.. It doesn't matter with the recirculation), turn it on, and forget about it.. I don't check nitrate, simply because I know where it is going to be.. It has been that way for years.. And it honestly, is a bit of a waste of time.. It is always at 0.5 because that's where I set the valves.. I check it maybe twice to three times a year, just to check it.. And I also have always run a fuge, and am now running an algea scrubber.. Both for phosphates and pod production.. And I've never had a problem doing so. I control that simply with a valve.. It's enough nitrate to keep color in my sps, and also to somewhat keep phosphate lowering going.. But I need the nitrate also to fuel plant growth in the cheato and scrubber.. Icontrol that once again with the valve.. But you have to understand how it works and how to control it.. Once you do that, it's easy with the right equipment.. But.. With pellets, you really need, and it will help tremendously to have the right equipment..
There are many ways to achieve the goal.. I also apologize for the long post. But natural is in the eye of the beholder.. Lol, there's really nothing truly natural about our systems.. We may want to think that, but we're have ocean life in an either glass, wood, or acrylic box.. All we can "try"to do is mimic and create something similar to their parameters.. I tend to have an open mind and try to think outside the box with this stuff, taking a multi pronged/hybrid approach, and it has worked well so far..
An example is now, my fuge is a 40 gallon stock tank.. I really hope to have that "literally"full of cheato, red Dragon, and purple grape algea.. This will do multiple things.. First, reduce nutrient to such a level to where gfo, is no longer needed at all, second, the red dragon and purple grape will be a nice treat for my tangs, third, the pod population in cheato is honestly insane, so my bug eaters will love me even more, fourth, the co2 levels will hopefully be low, and my ph will go up, which will counteract the calcium reactor low ph effluent, and lastly, it's a fun experiment(i love plants, and trying to accelerate growth) since I'm using high powered lights.. This is a bit off to your question, but at the same time it's not, because you spoke of control.. You have the control to do whatever you want and grow whatever you want..
But yes, recirculation is the way to go.. You control literally everything!
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