From my own personal experience of cleaning up our lake in Florida (South of Tampa),
Sounds like some physical activity with a buddy (watch out for each other) and some snorkel gear.
Lilly pads may take up a lot of surface area, but there is lots of room under. The roots can be larger than 3 to 4 (even more feet) long, but if you are not afraid of gators, you can go down and pull them out to create fishing lanes (the roots are long and grow horizontally and not down into the muck). I don't recall the Lilly pads growing into the deeper areas of the pond (not deeper than 8').
The big problem is the introduction of that 'Water Cabbage/lettuce' http://myfwc.com/wildlifehabitats/invasive-plants/weed-alerts/water-lettuce/
(which I can't believe they sell in stores that cater to Koi/pond enthusiast). My uncle picked up one in 1974 from the Alafia River (a favorite food of manatees...too bad you can't rent a manatee as they'd clean it up within a few weeks), and brought it home and put it in the pond, and by the 2nd year it was all over the surface, and the ducks/geese would introduce it to every body of water (creeks, and county ponds) in the area. We would spend weekends raking the water cabbage (acres of it) putting it in a pile and later burning it).
Every golf pond in Central Florida has healthy population of "Nile Perch" or Tilapia. I don't know how you could legally be permitted to obtain them. A single throw of a castnet, and I have easily caught 18 adults. A dozen of those in the pond, and not only would they consume the water plants, but they are a favorite food of Large Mouth Bass. They are also very good on your own table.
I believe you can also obtain grass carp, but I am not too familiar with that process.