What I'd suggest, based on your further info, is:

1) don't change the water again, even if you do have more blooms of blanket weed. Try to keep the same water year on year. Balance isn't an instantaneous thing, it's something that develops.

2) try to cover at least a third of the water surface with leaves. Don't cover all the surface, as this will mean the water stays too cold over the summer and will affect your tadpoles.

3) you could try barley straw, which I've had no experience with

4) as well as the plants you are using to shade part of the surface, grow something fast growing that will mop up nutrients, and pull it up every now and again and put it on the compost heap (thus transferring the nutrients out of the pond and hopefully on to your vegetables). Watercress is a possibility, as is water forget-me-not. Don't pull them up till towards the end of the summer - my newts use the water forget-me-not for egg laying, folding the leaves around the egg.