Hi there.
My tap water has a nitrate level of 40ppm, so my sympathies are with you here. I use a tap water/RO mix on some of my tanks, but not all of them (way too many). I'm currently looking onto ways to reduce my nitrate levels, and have bought some of the Seachem media. I'm under the impression that this won't have any impact on your levels immediately because the nitrate is used by anaerobic bacteria, which could take a while to build up to useful levels.
Substrate in my tanks is sand over planting substrate, with live plants, and although my tap water has high nitrates, I don't get any increase between the weekly water changes.
I also have plecs, and adorable as they are, they are also very messy.
I have some suggestions, and it would be useful to see what the others think before you consider taking on any of them.
To deal with the current algae problem I would consider blacking out the tank for several days. Blocking out all light should cause the algae start dying off.
At the same time I would start to do daily siphoning of waste, and try to scrape as much algae off decor as possible. Maintain weekly water changes & alternating filter cleans.
I would also consider removing the gravel. Not only because waste sits on top of a sand substrate, so it's easier to see to clean, but I've previously struggled to keep gravel clean if there is anything else underneath. That may have been more about my abilities (or lack of), but I found it difficult to keep the gravel clean enough, without removing the sand underneath whilst siphoning.
Once the algae has been dealt with (hopefully within a week or two), then floating plants would be useful when the lights are back on.
Dealing with tap water nitrite levels is a more long term issue, but at least we should be able to get to a point where your levels are not going up between water changes fairly quickly.
Would you be able to post some pictures of your tank, and provide as much information as possible about it (lighting periods, location - does it get any direct light, etc), and we'll see if we can make any more suggestions to resolve you issue.