What are your goals for the pond? If improved fishing & better weed control, deepening seems urgent. Usually the cheapest way is to raise the dam rather than digging out the muck.

Can't tell you what to do, obviously. But if it were me I'd drain, poison fish (green sunfish are size limited and tend to overcrowd), raise dam, add some habitat (trees, rocks) on pond bottom. My guess is that a 20 to 1 watershed to pond ratio near Nashville is adequate to refill, but you may want expert opinion on that. Then start over with fathead minnows first, then bluegill, then LMB. This will involve some expense, and you will lose your current fish, but otherwise the future sounds bleak.