Hi,
I think you have the following root causes:
1. Too MUCH light, period. It is NOT the duration so much as the intensity. MH are very bright bulbs. I assume you meant suspended 30cm and not 300? I would either raise the light or simply purchase a shop light for T8 or T5 and get some 6500 k tubes. This will provide better SPREAD of light and less intensity. 2-4 tube fixture would be great if tubes can be removed and the fixture still work.
LIGHT is what drive NUTRIENT and C02 DEMAND! The more light, the more demand

At higher light levels it can become very difficult to provide enough c02 required.
2. Filtration - filters are NOT all the same is all I will say. You do yourself a disservice with your assumption that they are more or less equivalent. You want to filter 5-10x the water volume as a good minimum. Many canisters do NOT produce the flow per mfg specs so be careful here. There are different types of canisters. Eheims for example are good bio filters but tend to flow much less water than say a Fluval or Magnum They are designed differently for different tasks. Many canisters are designed for mechanical filtration mostly and bio-filtration an afterthought.
Look at my recent video on my sump and CPR overflow for the operation of an overflow and sump for a non drilled tank....
http://www.barrreport.com/showthread.php/10717-Sump-and-CPR-Overview
3. Surface agitation - o2 is vital for plants and fish and is part of the c02 equation. More 02 allows for a bit more c02 and provides a bit more safety for fauna. A switch to a sump and overflow box will also provide surface skimming which has many advantages.
4. C02 - I would stop trying to use the kh/ph chart as it is not foolproof and can easily make you think you have plenty of c02 when in fact you do not. I would suggest that you do NOT have sufficient c02 as your issues highlight. There are more assumptions to the chart than you may know. Also, many hobbyist test kits are not that accurate. If they have NOT been calibrated to a known solution (a whole nother subject) you cannot use the results to make decisions.
5. EI dosing - dose N,P, and K and macros. Do so at least 3x per week with a 50% water change. It is very difficult to overdose and you seem to not have enough. It is not going to hurt anything to dose EI for a 150 gal tank say. This is where the 50% water changes come in to avoid a buildup. Trust me, I am sure I dose more than needed in my 220, but it dose no harm that I can see, and I can rule out these types of deficiencies.
Re, stop dosing of P. I do not understand at all the experimentation with limiting nutrients to induce color or reduce GSA. This simply causes a ripple effect in how the plant grows and functions. I would not do this with a fish or animal, why with a plant? It makes no sense to me....
Here is what I would do if this were my tank:
1. Dump the MH and go to flourescent or raise the MH fixture a lot! I had 3x150 mh years ago and they were suspended 40" above a 24" deep tank and still had 100mmoles of PAR at the substrate which is very high light. You can have a 6-8 hr CONSTANT photoperiod. Then use say 1 tube for off hours viewing. With say a 4 tube fixture, you can use the 2 outer bulbs for a good spread over the tank and perhaps not need the inners.
But when things are better, you can use the other 2 for a short 'noon' burst if you so desire.
You can also use floating plants to shield the light or use screening material in layers to reduce the light.
2. Dose EI at DOUBLE the recommend rate. Dose AFTER your water change. Try for 2-3 x weekly, but daily is better if you can do so. It takes 2 minutes!!!! I used to be really bad at this but stuck with it and am now a regular daily doser. Mix ferts in cup of water, stir, and dump in sump.
3. Do larger 75% water change with dechlorinator/Prime as needed for the FULL TANK volume. For now the more water changes the better. Daily would be best but 2 or 3 weekly will help a lot for the next say 2-3 weeks.
4. Get another filter. This can act as a spare and improve tank flow. This will also obviously increase your current filtration level which is not a bad thing. It is very hard to overfilter a tank. Or swap to a good sized wet dry and sump.
5. Increase C02 slowly a tiny bit and then OBSERVE fish and critters for signs of stress. Make an adjustment every 4-5 days with observation in between.
You may also want to investigate other methods of c02 diffusion such as a NW (needle wheel) pump. Your reactor may also be undersize or inefficient for the tank size.
6. Investigate a sump with a HOB overflow box. No need to drill a tank to install a sump and wet/dry.
7. Manually remove as much of the algae as possible.
8. Remove any algae infested or dead/decaying leaves. These will not regrow so eliminate them. Replace any bunches of plants beyond repair. Get some new ones, check forum sales for plants as these can be better quality/less cost. Get some water wisteria, hygro species, etc that will grow quickly.
Steps 2-5 can be done for several weeks to assess the results and ensure all is well with the increased c02.
Your BGA can be caused by low K, dirty or underperforming filters, low c02 or any combination of these three.
I really think you are underdosing, underfiltered, overlit, most likely insufficent c02, and not enough in tank flow or surface agitation.
Have some PATIENCE as well. It will take some time for the plants to recover and the algae to stop growing. Watch your plants for signs of new growth and no more NEW algae. This may take some time to get it all working as you want. C02 is NOT easy to guage and it is a fish/critter killer, so much care must be taken.
I am curious as to what changed since your move that your well run tank fell apart? To what do you attibute all these issues? What type of advice did you receive and what were the results? The tank should be cycled/mature by now after 8 mos. To go from trimming a bucket of plants a week to the tank I see above is pretty drastic.
Hope this helps.