Fishy - I would advise against adding more GC - it's trying to one's patience allowing the "organic" vegetation management solution to work, but I feel 6 for a .75 ac BOW is sufficient. You don't want a pond denuded of vegetation which turns into a turbid mess then having to deal with GC removal, which by all accounts, is a difficult process.
If you are interested in constructing a beach, staple landscape fabric first and build a 12" ridge around the entire area. The fabric prevents vegetation from growing in your beach area, and the ridge keeps sand in place and prevents it from washing out. Think 12-24" of sand/gravel or whatever substrate feels best to your toes. Several accounts on PB forum which detail this process.
CLPW I have experience with - since it dies out pretty early I have never felt compelled to manage for it. However, I have treated some dense colonies of baby pondweed and coontail this Spring in areas around my dock and feeder with Aquathol Super K granules [based on expert direction from Kelly]. It worked amazingly well and I was astounded by it's prompt effectiveness, but it's pricier than regular Aquathol which the manufacturer states is very effective on CLPW. If you want to clear some areas, I think you could use the lower priced AQTL option and see similarly impressive results. I would advise against using Fluridone as it will indiscriminately nuke all vegetation in your pond, submergent and emergent - beneficial or invasive. Unless that's your goal and you have a runaway issue, I'd recommend allowing the GC to do their thing, or try spot treatment in areas with the cheaper Aquathol product.