Well, you are back to trying to figure out what the city water is offering to the tank.
However, when in doubt, dose more then do a large water change would normally be my suggestion. That way you know the plants are not deficient for the things that you can control.
ANY water change (no matter if the tap water is really stable from week to week or variable) will create changing levels of nutrients for the tank.
Given that your lights are getting old that might be another issue to address. If you are still seeing the light as 'OK', that does not mean that it is still OK through the whole spectrum. The plant specific wavelengths may have dropped off more than you think.
If you are having problems with the CO2, then I think that is more important than the fertilizers.
I would address things in this order:
Fix the lights (new bulbs)
Fix the CO2
Dose something like EI (no limiting ferts, no matter what the tap water is doing)
Remove algae by hand
Then monitor the tank for plant growth and algae.
Continue to record the variations in the tap water so you can figure out if you need to alter something. If you find something you want to alter, then do this before the water change, run the water into a barrel and do whatever changes you feel will help.
Another thing you can look into is reverse osmosis for the house. This will remove the 'variable tap water' from the puzzle.