Do you know for sure your soil is low in Mn though? Ordinarily it's there but blocked by the pH and a pH of 7.1 is enough to do that to manganese. I would not add manganese to the soil without a test, like some other micronutrients it is essential but only in small quantities and is toxic to plants in higher amounts. In most cases lowering the pH will make sufficient manganese (and other micros) more available to the plants.
No, you don't want to use dolomite because it could raise the pH even higher and make micronutrients even less available. But since you mentioned dolomite, which is a source of magnesium, just double checking that you do mean manganese sulfate and not magnesium sulfate (Epsom salts)?
