Jim,
you're not whining, you're frustrated! I would be, too. Taking things from a simple, logical point of view, in order to have algae growth, there must be nutrients somewhere to allow this growth. Not necessarily a bad thing. Some nutrients must be present. I do have algae growth in my tanks, some quite a bit, depending on the type of environment, but there are animals in there that feed on the algaes and bacterial films. Therfore they tend to constantly disappear. If nothing ate these things, they would be a problem.
Now, getting back to the nutrient source, if this is simply stored in the rocks, it will go away in time, but the left-overs from the algaes will take a lot longer to disappear. They do not simply dissolve into the water column, they need to be eaten by something (bacteria to fish). Which brings me to general tank population.
Judging from the fotos you sent, you have relatively little going on in the tank at the moment. More life will compete with the algaes for space and available nutrients. I would consider what types of creatures I want to see and which one I really need to maintain a reef-type environment. More corals is clear, but smaller animals, such as crustaceans, featherdusters, sea stars (brittle stars) can all be a part of the set-up and will help to maintain the reef.
As to your first question, maintaining a tank without a zeolith filter, yes, there are more ways than one to approach the system. A zeolith filter is a controlable, bio-entity, which is why we use them. It will not out-compete (over-filter), as long as it is in proportion to the bio-load. (your bio-load is too low and doesn't contain enough variety, IMO). I'm not sure you have grasped the difference between the filter itself and the carbon dosing. They are completely different items, partly interdependant on each other. You can run a system with just carbon dosing and no zeolith filter. It will not have the capacity to maintain much diverse life, but it will work after a fashion. Some people use a DSB with carbon dosing, which is very difficult to control. The zeolith is simply a filter medium. Yes, it has particular qualities that make it especially good for such a filter system, but there are other alternatives, such as siporax or similar. They have good capacity, but are not quite as effective in most cases (there is a debate going on over various filter materials, as typical). The bottom line is, a filter is an important part of any system. It's controlability is a major factor in choosing the type of filter. The carbon source is simply a food for the bacteria, nothing more. It is not a filter. You can have the carbon dosing by itself with a limiter capacity to maintain a bio-system. The filter allows one to increase this capacity by raising the efficiency of the bacterial system. By controling the amount of carbon dosed, one can control the efficiency fo the filter.
Things that one should not do are to make any quick, drastic changes in the filter system. Slowly raise or lower the carbon dose, or the water flow through the filter. The same goes for adding animals to the system. Not too may at one time and keep an eye on the nutrient levels. A healthy system is actually very adaptable and flexible, but everything has its limits.
Also, I am still suspect of the nutrient levels. I would try to get another test kit for the PO4, such as that from Rowa, which is much more accurate than the Elos. I have often found that there were considerable amounts of PO4 not being read by the Elos kit. I like Elos, but this kit is simply not their best. Try at your fav fish store and see if they have something better. I have often read 0 PO4 with a kit and then tested with Rowa and had 0.14 PO4, which is at that critical level that feeds algaes particularly well. I may be wrong, but this is for me a bit strange. One should always test something present, otherwise the kit is not accurate enough.
I think you know most of this, but restating it differently often makes a new picture and clears a few more questions. I wish I could help you better, really.
