Reefle,
You have a long road ahead, so don't get discouraged just yet
I completely understand your wish to cut down on water changes. I believe this will be possible in time, but for now it's probably not a bad idea to go ahead with it. You have to let your tank establish the correct sized bacteria "buffer" before you can be all cool and go without changing water often.
In my experience, high nitrates means one, and only one thing, which translates to you not having enough surface area for beneficial bacteria to grow. In your case specifically, you don't have near the amount of live rock that you need. Since you are working on remedying that, I think you'll be surprised how quickly your nitrate issue resolves over time. In a few months, you'll be able to develop your own water change/not water change schedule and figure out all the wackadoodle stuff that goes on with water chemistry.
In the long term however, I would also advocate at least researching the algae scrubber. Pay special attention to the mat size (growing surface) and the proper amount of light. It's easy to provide too little or too much. This particular item was an excellent solution for my setup, although I was battling phosphates more than nitrates. In fact, I've never had detectable nitrates since about 2003.
Phosphates on the other hand have been an ongoing struggle, until about the last two years or so.
I'll likely get flamed for this, but I don't care because I know it to be true in MY particular case. In the long term, battling nitrate or phosphates with water changes is sort of like trying to keep calcium and alk up in the same manner. You can do it that way, but there are much easier ways of dealing with these problems.
Very minute levels of phosphate are purported to cause issues, and it's usually very minute amounts that exist in our aquaria. Even what we consider "high" is so diluted, that doing a large water change does little good. For example, the basic rule is to strive for <.03. Let's say it's .05. We do a 50% water change, and now we are at .025%, barely enough to get below the minimum accepted level. Not very economical. And, it's easy for phosphate to rise quickly.
The same could be said about nitrates, but I look at nitrates differently than most others. In my experience, unless nitrates are excessively high (50+ppm), these levels are not neccessarily lethal, even for the most sensitive to it. (Inverts and coral.) Now I'm not saying not to pay attention to nitrate levels if they rise - by all means, keep them as low as possible. But, I think there is sometimes too much emphasis on nitrate levels. Corals, clams, and other life in reefs actually REQUIRE nitrates to survive, although these amounts are usually much less than you would find in an aquarium. It's much easier to drop nitrates with water changes than with phosphates, and in your case it may be required. I would shoot for below 10 at all times if you can.
Back in the late 90's, we were all focused on nitrate removal for the hair algae battles. Now it's all about phosphates. What will it be tomorrow? LOL
Feed less. I like to keep my fish hungry and coral hungry, but not emaciated. With your nitrate levels as high as they are and the amount of stock you have, I would cut feeding way down - to like three times a week for now. Your fish will not starve and die. Once your rock takes your nitrates down (while you are doing partial water changes to help it along), you'll be able to feed more.
Everything will fall into place. You'll see.
