Ag lime would probably be a big plus for your pond, but get a water test showing alkalinity, hardness and pH along with a soil test from a mixture of soils in the pond and surrounding drained areas to know how may tons of lime are needed (if needed at all).
I am really surprised to hear your water clears in jar tests, you look to have a lot of grass filtering runoff and erosion does not look too bad from wind/wave action either. Your pond may still be a good candidate for a mild Alum treatment to make it clear, reclear faster and allow a nice bloom to take hold.
