I use a Taylor K-2005 test kit and it includes a 'Watergram' wheel that helps establish water balance. This is a slide rule type device which calculates LSI (Langelier Saturation Index; Google it). In a nutshell - Calcium, Total Alkalinity, pH, and Temperature are like four legs of a chair and this chair wobbles and can almost never be made to sit perfectly level on the ground, particularly in a volume of water that is open to the elements. One factor that is rarely in this calculation is Total Dissolved Solids (TDS) which based on your story, I assume it is probably way high. If it is over 2000ppm then you are due for a complete or partial drain and refill. If you are using well water and its balance is off, it may be adding to the problem. I suggest you take samples of your pool water and tap water and send it off for a full water quality test. TDS is a pain to measure accurately but cheap electronic meters are available for $20 or so that will get you a ballpark measurement. The other ballbark measurement is the taste of the water - if its salty or minerally sweet then its worth checking.
The other thing is that Cyanuric Acid makes the TA measurement inaccurate. The simple rule is
Actual TA = TA - (CyA/3). This varies by pH as well but the last page of my Taylor kit manual says if your pH is 7.2 then the formula is
Actual TA = TA - (CyA*0.26) and if the pH is at 7.5 (your target) then the 1/3 is correct. If CyA is over 150ppm then you need a drain and refill. (Some local health departments limit it to 100ppm, and there are some claims that CyA may be a carcinogen)
CyA (Cyanuric Acid) is part of the Trichlor molecule and has the effect of preventing sunlight from destroying Chlorine but if CyA is over 40ppm, it is not any more effective at doing so. Therefore to me, it makes sense to use Trichlor until you get to 40ppm and then switch to some other method, like bleach or higher concentrated Sodium Hypochlorite from the pool store. Even better, and since you have algae growth, is to pay someone to come in with Chlorine gas tanks and superchlorinate it to 30ppm. It will make the pool unusable for a day or more and you'll probably want to make a day trip somewhere with all the kids and pets and warn all the neighbors while the pros do their thing. This will also blow away all the Chloramines (Combined Chlorine) which may be another part of your problem.
You don't mention your Calcium reading but you do say you have white stuff on the edge meaning its scaling. If your water is too high in Calcium then the only way to get rid of it is to drain and refill, either partially or completely. This can be exasperated if your system includes an autofiller and you have a lot of evaporation and also if your tap/well water is high in calcium to begin with (hard water).
Most instructions pool owners receive to simply keep all of these measurements within a certain range and typically this will result in the near balanced water. If you have excel or other spreadsheet, you can do alot better. Here is a formula that calculates LSI which tells you your water balance (scale formation/dissolution potential):
=9.3+(0.1*(LOG10(B1)-1))+(-13.12*LOG10((B2+459.67)*5/9 )+34.55)-((LOG10(B3)-0.4)+LOG10(B4))B1 = TDS (Assume 200ppm if its unknown)
B2 = Water Temperature in Farenheit (
(B2+459.67)*5/9 converts F to Kelvin)
B3 = Calcium Hardness
B4 = TA corrected for CyA
The resulting number is the pH of Saturation and if you subtract the measure pH from this number then the result is the LSI. The LSI needs to be within +/- 0.5 of Zero. Large Positive Values mean that white stuff on the edge of the pool, Large Negative values mean the water will dissolve the white stuff and possibly concrete and metalwork along with it.
http://www.corrosion-doctors.org/Cooling-Water-Towers/Index-Langelier.htm The nice thing about having it in a spreadsheet is you can play with the factors you can easily control - TA, Calcium Hardness, and pH and get it to a near Zero LSI. Once that is in control, sanitation concerns are much more easily dealt with.