Interesting question. Chara isn't an invasive plant. When water levels drop, it makes chara look bad. During 'normal' conditions, chara rarely manifests itself at the surface. Unless it covers more than 25% of your pond bottom, I would leave it alone, especially this time of year. If you eradicate chara, you openly invite other plants, most of the time more invasive than the chara ever hoped to be.
Regarding water amendments, you trade problems. More acidic water invites plants which grow in acidic water.
As you will see, if you research our site, there are three keys to plant growth. Sunlight, food, and temperature. When those three come together SOMETHING will grow.
Personally, I would pick chara over many, many plants.
