Okay, I'll try to go in order.
Nitrates at 80 is WAAAAY to high.. As mentioned before, Mr. Condi won't like that at all. As will all inverts.
Nitrates in a tank holding inverts (nems, shrimp, crab, corals etc.) Should be single digits. Some will argue a bit more, bit I digress...
I would trust API as far as I could throw my car... Just my opinion, but still...
A dead spot on the surface won't affect Nitrate. More of a gas exchange situation, but still important.
30 gals in a 125 would be close to the ratio of what I personally do weekly. I think if you could do that for a few weeks, you would see a marked improvement in your Nitrate levels. So you have a comparison, I do 55 gals on my 240 weekly. Some may argue this point, but as I mentioned earlier, what works for one may not work for another... At the end, all boils down to water quality.
As far as the "sugar theory" that is a type of carbon dosing. Sugar is a type of carbon as is vodka and Bio pellets. I think a basic understanding of how YOUR tank works with bio load etc. with a regular water change schedule, high quality test kits and a bit of patients, will go much further than adopting a fancy biological method you may not fully understand. I am not meaning to pick on you,or demean carbon dosing all, but there is quite a bit more to carbon dosing than dumping a bit of sugar, vodka or whatever in the tank.
Hope this didn't sound like preaching, or a long winded diatribe...
Keep the questions coming. I am more than sure many here will add (or possibly contradict) everything I and others have said. Keep in mind. LOOK at your tank and inhabitants. They will more often than not tell you how they feel... Work from sound basic principles, don't rush to judgment. You'll be fine. So will your tank...