Might be even crazier. If you want something cheap that floats a long time in the ocean you probably need to make it of glass, not plastic. Recycled broken glass could be re-melted and formed into sealed cylindrical floats 12-inches by 24-inches giving a displacement of 1.57 cu feet. Each glass float would provide about 100-pounds of gross buoyancy. The float itself would weigh about 32-pounds, so each glass float would provide 68-pounds of payload buoyancy. Truckloads of scrap glass should sell for less than $100/ton; so, raw material cost for a ton of scrap glass float payload buoyancy would be about $35. The glass floats would need to transfer their buoyancy to the main structure, which would need to be fashioned of some cost effective marine environment stainless steel, such as 2205. As attractive as all that might sound, glass is only strong in compression. It’s brittle and weak in tension so float attachment systems would have to avoid tension loads. Seems likely no “scrap” material would be as cost effective as just building new barges out of 2205 stainless, which should hold up for a couple of centuries.

The only way to solve the gyre garbage dump problem is for all major nations to impose stiff penalties for ocean dumpers (you can’t trade in our ports if you dump in the oceans!), and if you really want to clean up the mess you would need hundreds of special built nuclear powered skimmer ships collecting and pyrolytically destroying the garbage for a decade or so. This is a case where dilution is probably a fair solution. Just impose standards that there is no dumping of anything that floats or which won’t promptly decompose. The annual carbon load into the atmosphere of burning all flammable garbage at sea would be trivial in contrast to global burning of fossil fuels.