I've been relatively active on homebrewtalk.com, have read the cleaning chapter of How to Brew half a dozen times, and watched the instructional video that came with my kit on how to clean carboys. I let them sit filled with hot water and LD Carlson's Easy Clean (which I'm pretty sure is PBW-equivalent) overnight, rinsed them out several times, took the carboy brush to them, and there's still tiny, stubborn particulates that just want to stick to the side of the glass and not come out. What can I do about this?
Use PBW - it'll shift pretty much anything without requiring any scrubbing.
LD Carlson's Easy Clean is not the same as PBW. Easy Clean is an oxygen-based cleaner, while PBW is an alkali-based cleaner.
I've used both, and can say without doubt that PBW is much better for cleaning carboys. With PBW the hot water is not strictly necessary, but it does help loosen sticky sugar-based soilage.